# Release notes¶

orphan

## Release 0.30.0-dev (development release)¶

### New features since last release

• The sample_state function is added to devices/qubit that returns a series of samples based on a given state vector and a number of shots. (#3720)

• Added the needed functions and classes to simulate an ensemble of Rydberg atoms:

• A new internal RydbergHamiltonian class is added, which contains the Hamiltonian of an ensemble of Rydberg atoms.

• A new user-facing rydberg_interaction function is added, which returns a RydbergHamiltonian containing the Hamiltonian of the interaction of all the Rydberg atoms.

• A new user-facing drive function is added, which returns a ParametrizedHamiltonian (HardwareHamiltonian) containing the Hamiltonian of the interaction between a driving electro-magnetic field and a group of qubits. (#3749) (#3911) (#3930)

• Added Operation.__truediv__ dunder method to be able to divide operators. (#3749)

• The simulate function added to devices/qubit now supports measuring expectation values of large observables such as qml.Hamiltonian, qml.SparseHamiltonian, qml.Sum. (#3759)

### Improvements

• Improve the efficiency of tapering(), tapering_hf() and clifford(). (3942)

• Update Pauli arithmetic to more efficiently convert to a Hamiltonian. (#3939)

• Keras and Torch NN modules are now compatible with the new return type system. (#3913) (#3914)

• The adjoint differentiation method now supports more operations, and does no longer decompose some operations that may be differentiated directly. In addition, all new operations with a generator are now supported by the method. (#3874)

• The coefficients function and the visualize submodule of the qml.fourier module now allow assigning different degrees for different parameters of the input function. (#3005)

The arguments degree and filter_threshold to qml.fourier.coefficients previously were expected to be integers, and now can be a sequences of integers with one integer per function parameter (i.e. len(degree)==n_inputs), resulting in a returned array with shape (2*degrees[0]+1,..., 2*degrees[-1]+1). The functions in qml.fourier.visualize accordingly accept such arrays of coefficients.

• Operator now has a has_generator attribute that returns whether or not the operator has a generator defined. It is used in qml.operation.has_gen, improving its performance. (#3875)

• The custom JVP rules in PennyLane now also support non-scalar and mixed-shape tape parameters as well as multi-dimensional tape return types, like broadcasted qml.probs, for example. (#3766)

• The qchem.jordan_wigner function is extended to support more fermionic operator orders. (#3754) (#3751)

• AdaptiveOptimizer is updated to use non-default user-defined qnode arguments. (#3765)

• Adds logic to qml.devices.qubit.measure to compute the expectation values of Hamiltonian and Sum in a backpropagation compatible way. (#3862)

• Use TensorLike type in Operator dunder methods. (#3749)

• The apply_operation function added to devices/qubit now supports broadcasting. (#3852)

• qml.QubitStateVector.state_vector now supports broadcasting. (#3852)

• pennylane.devices.qubit.preprocess now allows circuits with non-commuting observables. (#3857)

• When using Jax-jit with gradient transforms the trainable parameters are correctly set (instead of every parameter to be set as trainable), and therefore the derivatives are computed more efficiently. (#3697)

• qml.SparseHamiltonian can now be applied to any wires in a circuit rather than being restricted to all wires in the circuit. (#3888)

• Added max_distance keyword argument to qml.pulse.rydberg_interaction to allow removal of negligible contributions from atoms beyond max_distancefrom each other. (#3889)

• 3 new decomposition algorithms are added for n-controlled operations with single-qubit target, and are selected automatically when they produce a better result. They can be accessed via ops.op_math.ctrl_decomp_bisect. (#3851)

• repr for MutualInfoMP now displays the distribution of the wires between the two subsystems. (#3898)

• Changed Operator.num_wires from an abstract value to AnyWires. (#3919)

• Do not run qml.transforms.sum_expand in Device.batch_transform if the device supports Sum observables. (#3915)

• CompositeOp now overrides Operator._check_batching, providing a significant performance improvement. Hamiltonian also overrides this method and does nothing, because it does not support batching. (#3915)

• If a Sum operator has a pre-computed Pauli representation, is_hermitian now checks that all coefficients are real, providing a significant performance improvement. (#3915)

• The type of n_electrons in qml.qchem.Molecule is set to int. (#3885)

• Added explicit errors to QutritDevice if classical_shadow or shadow_expval are measured. (#3934)

• DefaultQutrit supports the new return system. (#3934)

• QubitDevice now defines the private _get_diagonalizing_gates(circuit) method and uses it when executing circuits. This allows devices that inherit from QubitDevice to override and customize their definition of diagonalizing gates. (#3938)

### Breaking changes

• Both JIT interfaces are not compatible with Jax >0.4.3, we raise an error for those versions. (#3877)

• An operation that implements a custom generator method, but does not always return a valid generator, also has to implement a has_generator property that reflects in which scenarios a generator will be returned. (#3875)

• Trainable parameters for the Jax interface are the parameters that are JVPTracer, defined by setting argnums. Previously, all JAX tracers, including those used for JIT compilation, were interpreted to be trainable. (#3697)

• The keyword argument argnums is now used for gradient transform using Jax, instead of argnum. argnum is automatically converted to argnums when using JAX, and will no longer be supported in v0.31. (#3697) (#3847)

• Made qml.OrbitalRotation and consequently qml.GateFabric consistent with the interleaved Jordan-Wigner ordering. Previously, they were consistent with the sequential Jordan-Wigner ordering. (#3861)

• Some MeasurementProcess classes can now only be instantiated with arguments that they will actually use. For example, you can no longer create StateMP(qml.PauliX(0)) or PurityMP(eigvals=(-1,1), wires=Wires(0)). (#3898)

### Documentation

• A typo was corrected in the documentation for introduction to inspecting_circuits and chemistry. (#3844)

### Bug fixes

• Fixed a bug where calling Evolution.generator with coeff being a complex ArrayBox raised an error. (#3796)

• MeasurementProcess.hash now uses the hash property of the observable. The property now depends on all properties that affect the behaviour of the object, such as VnEntropyMP.log_base or the distribution of wires between the two subsystems in MutualInfoMP. (#3898)

• The enum measurements.Purity is added so that PurityMP.return_type is defined. str and repr for PurityMP are now defined. (#3898)

• Sum.hash and Prod.hash are slightly changed to work with non-numeric wire labels. sum_expand should now return correct results and not treat some products as the same operation. (#3898)

• Fixed bug where the coefficients where not ordered correctly when summing a ParametrizedHamiltonian with other operators. (#3749) (#3902)

• The metric tensor transform is fully compatible with Jax and therefore users can provide multiple parameters. (#3847)

• Registers math.ndim and math.shape for built-ins and autograd to accomodate Autoray 0.6.1. #3864

• Ensure that qml.data.load returns datasets in a stable and expected order. (#3856)

• The qml.equal function now handles comparisons of ParametrizedEvolution operators. (#3870)

• Made qml.OrbitalRotation and consequently qml.GateFabric consistent with the interleaved Jordan-Wigner ordering. (#3861)

• qml.devices.qubit.apply_operation catches the tf.errors.UnimplementedError that occurs when PauliZ or CNOT gates are applied to a large (>8 wires) tensorflow state. When that occurs, the logic falls back to the tensordot logic instead. (#3884)

• Fixed parameter broadcasting support with qml.counts in most cases, and introduced explicit errors otherwise. (#3876)

• An error is now raised if a QNode with Jax-jit in use returns counts while having trainable parameters (#3892)

• A correction is added to the reference values in test_dipole_of to account for small changes (~2e-8) in the computed dipole moment values, resulting from the new PySCF 2.2.0 release. (#3908)

• SampleMP.shape is now correct when sampling only occurs on a subset of the device wires. (#3921)

### Contributors

This release contains contributions from (in alphabetical order):

Komi Amiko Utkarsh Azad Lillian M. A. Frederiksen Soran Jahangiri Christina Lee Vincent Michaud-Rioux Albert Mitjans Romain Moyard Mudit Pandey Matthew Silverman Jay Soni David Wierichs

orphan

## Release 0.29.0 (current release)¶

### New features since last release

#### Pulse programming 🔊

• Support for creating pulse-based circuits that describe evolution under a time-dependent Hamiltonian has now been added, as well as the ability to execute and differentiate these pulse-based circuits on simulator. (#3586) (#3617) (#3645) (#3652) (#3665) (#3673) (#3706) (#3730)

A time-dependent Hamiltonian can be created using qml.pulse.ParametrizedHamiltonian, which holds information representing a linear combination of operators with parametrized coefficents and can be constructed as follows:

from jax import numpy as jnp

f1 = lambda p, t: p * jnp.sin(t) * (t - 1)
f2 = lambda p, t: p[0] * jnp.cos(p[1]* t ** 2)

XX = qml.PauliX(0) @ qml.PauliX(1)
YY = qml.PauliY(0) @ qml.PauliY(1)
ZZ = qml.PauliZ(0) @ qml.PauliZ(1)

H =  2 * ZZ + f1 * XX + f2 * YY

>>> H
ParametrizedHamiltonian: terms=3
>>> p1 = jnp.array(1.2)
>>> p2 = jnp.array([2.3, 3.4])
>>> H((p1, p2), t=0.5)
(2*(PauliZ(wires=[0]) @ PauliZ(wires=[1]))) + ((-0.2876553231625218*(PauliX(wires=[0]) @ PauliX(wires=[1]))) + (1.517961235535459*(PauliY(wires=[0]) @ PauliY(wires=[1]))))


The time-dependent Hamiltonian can be used within a circuit with qml.evolve:

def pulse_circuit(params, time):
qml.evolve(H)(params, time)
return qml.expval(qml.PauliX(0) @ qml.PauliY(1))


Pulse-based circuits can be executed and differentiated on the default.qubit.jax simulator using JAX as an interface:

>>> dev = qml.device("default.qubit.jax", wires=2)
>>> qnode = qml.QNode(pulse_circuit, dev, interface="jax")
>>> params = (p1, p2)
>>> qnode(params, time=0.5)
Array(0.72153819, dtype=float64)
(Array(-0.11324919, dtype=float64),
Array([-0.64399616,  0.06326374], dtype=float64))


Check out the qml.pulse documentation page for more details!

#### Special unitary operation 🌞

• A new operation qml.SpecialUnitary has been added, providing access to an arbitrary unitary gate via a parametrization in the Pauli basis. (#3650) (#3651) (#3674)

qml.SpecialUnitary creates a unitary that exponentiates a linear combination of all possible Pauli words in lexicographical order — except for the identity operator — for num_wires wires, of which there are 4**num_wires - 1. As its first argument, qml.SpecialUnitary takes a list of the 4**num_wires - 1 parameters that are the coefficients of the linear combination.

To see all possible Pauli words for num_wires wires, you can use the qml.ops.qubit.special_unitary.pauli_basis_strings function:

>>> qml.ops.qubit.special_unitary.pauli_basis_strings(1) # 4**1-1 = 3 Pauli words
['X', 'Y', 'Z']
>>> qml.ops.qubit.special_unitary.pauli_basis_strings(2) # 4**2-1 = 15 Pauli words
['IX', 'IY', 'IZ', 'XI', 'XX', 'XY', 'XZ', 'YI', 'YX', 'YY', 'YZ', 'ZI', 'ZX', 'ZY', 'ZZ']


To use qml.SpecialUnitary, for example, on a single qubit, we may define

>>> thetas = np.array([0.2, 0.1, -0.5])
>>> U = qml.SpecialUnitary(thetas, 0)
>>> qml.matrix(U)
array([[ 0.8537127 -0.47537233j,  0.09507447+0.19014893j],
[-0.09507447+0.19014893j,  0.8537127 +0.47537233j]])


A single non-zero entry in the parameters will create a Pauli rotation:

>>> x = 0.412
>>> theta = x * np.array([1, 0, 0]) # The first entry belongs to the Pauli word "X"
>>> su = qml.SpecialUnitary(theta, wires=0)
>>> rx = qml.RX(-2 * x, 0) # RX introduces a prefactor -0.5 that has to be compensated
>>> qml.math.allclose(qml.matrix(su), qml.matrix(rx))
True


This operation can be differentiated with hardware-compatible methods like parameter shifts and it supports parameter broadcasting/batching, but not both at the same time. Learn more by visiting the qml.SpecialUnitary documentation.

#### Always differentiable 📈

• The Hadamard test gradient transform is now available via qml.gradients.hadamard_grad. This transform is also available as a differentiation method within QNodes. (#3625) (#3736)

qml.gradients.hadamard_grad is a hardware-compatible transform that calculates the gradient of a quantum circuit using the Hadamard test. Note that the device requires an auxiliary wire to calculate the gradient.

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit(params):
...     qml.RX(params[0], wires=0)
...     qml.RY(params[1], wires=0)
...     qml.RX(params[2], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> params = np.array([0.1, 0.2, 0.3], requires_grad=True)


This transform can be registered directly as the quantum gradient transform to use during autodifferentiation:

>>> dev = qml.device("default.qubit", wires=2)
... def circuit(params):
...     qml.RX(params[0], wires=0)
...     qml.RY(params[1], wires=0)
...     qml.RX(params[2], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> params = jax.numpy.array([0.1, 0.2, 0.3])
>>> jax.jacobian(circuit)(params)
Array([-0.3875172 , -0.18884787, -0.38355705], dtype=float32)

• The gradient transform qml.gradients.spsa_grad is now registered as a differentiation method for QNodes. (#3440)

The SPSA gradient transform can now be used implicitly by marking a QNode as differentiable with SPSA. It can be selected via

>>> dev = qml.device("default.qubit", wires=1)
>>> @qml.qnode(dev, interface="jax", diff_method="spsa", h=0.05, num_directions=20)
... def circuit(x):
...     qml.RX(x, 0)
...     return qml.expval(qml.PauliZ(0))
>>> jax.jacobian(circuit)(jax.numpy.array(0.5))
Array(-0.4792258, dtype=float32, weak_type=True)


The argument num_directions determines how many directions of simultaneous perturbation are used and therefore the number of circuit evaluations, up to a prefactor. See the SPSA gradient transform documentation for details. Note: The full SPSA optimization method is already available as qml.SPSAOptimizer.

• The default interface is now auto. There is no need to specify the interface anymore; it is automatically determined by checking your QNode parameters. (#3677) (#3752) (#3829)

import jax
import jax.numpy as jnp

qml.enable_return()
a = jnp.array(0.1)
b = jnp.array(0.2)

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(a, b):
qml.RY(a, wires=0)
qml.RX(b, wires=1)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliY(1))

>>> circuit(a, b)
(Array(0.9950042, dtype=float32), Array(-0.19767681, dtype=float32))
>>> jac = jax.jacobian(circuit)(a, b)
>>> jac
(Array(-0.09983341, dtype=float32, weak_type=True), Array(0.01983384, dtype=float32, weak_type=True))

• The JAX-JIT interface now supports higher-order gradient computation with the new return types system. (#3498)

Here is an example of using JAX-JIT to compute the Hessian of a circuit:

import pennylane as qml
import jax
from jax import numpy as jnp

jax.config.update("jax_enable_x64", True)

qml.enable_return()

dev = qml.device("default.qubit", wires=2)

@jax.jit
@qml.qnode(dev, interface="jax-jit", diff_method="parameter-shift", max_diff=2)
def circuit(a, b):
qml.RY(a, wires=0)
qml.RX(b, wires=1)
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))

a, b = jnp.array(1.0), jnp.array(2.0)

>>> jax.hessian(circuit, argnums=[0, 1])(a, b)
(((Array(-0.54030231, dtype=float64, weak_type=True),
Array(0., dtype=float64, weak_type=True)),
(Array(-1.76002563e-17, dtype=float64, weak_type=True),
Array(0., dtype=float64, weak_type=True))),
((Array(0., dtype=float64, weak_type=True),
Array(-1.00700085e-17, dtype=float64, weak_type=True)),
(Array(0., dtype=float64, weak_type=True),
Array(0.41614684, dtype=float64, weak_type=True))))

• The qchem workflow has been modified to support both Autograd and JAX frameworks. (#3458) (#3462) (#3495)

The JAX interface is automatically used when the differentiable parameters are JAX objects. Here is an example for computing the Hartree-Fock energy gradients with respect to the atomic coordinates.

import pennylane as qml
from pennylane import numpy as np
import jax

symbols = ["H", "H"]
geometry = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]])

mol = qml.qchem.Molecule(symbols, geometry)

args = [jax.numpy.array(mol.coordinates)]

>>> jax.grad(qml.qchem.hf_energy(mol))(*args)
Array([[ 0.       ,  0.       ,  0.3650435],
[ 0.       ,  0.       , -0.3650435]], dtype=float64)

• The kernel matrix utility functions in qml.kernels are now autodifferentiation-compatible. In addition, they support batching, for example for quantum kernel execution with shot vectors. (#3742)

This allows for the following:

dev = qml.device('default.qubit', wires=2, shots=(100, 100))
@qml.qnode(dev)
def circuit(x1, x2):
qml.templates.AngleEmbedding(x1, wires=dev.wires)
return qml.probs(wires=dev.wires)

kernel = lambda x1, x2: circuit(x1, x2)


We can then compute the kernel matrix on a set of 4 (random) feature vectors X but using two sets of 100 shots each via

>>> X = np.random.random((4, 2))
>>> qml.kernels.square_kernel_matrix(X, kernel)[:, 0]
tensor([[[1.  , 0.86, 0.88, 0.92],
[0.86, 1.  , 0.75, 0.97],
[0.88, 0.75, 1.  , 0.91],
[0.92, 0.97, 0.91, 1.  ]],
[[1.  , 0.93, 0.91, 0.92],
[0.93, 1.  , 0.8 , 1.  ],
[0.91, 0.8 , 1.  , 0.91],
[0.92, 1.  , 0.91, 1.  ]]], requires_grad=True)


Note that we have extracted the first probability vector entry for each 100-shot evaluation.

#### Smartly decompose Hamiltonian evolution 💯

• Hamiltonian evolution using qml.evolve or qml.exp can now be decomposed into operations. (#3691) (#3777)

If the time-evolved Hamiltonian is equivalent to another PennyLane operation, then that operation is returned as the decomposition:

>>> exp_op = qml.evolve(qml.PauliX(0) @ qml.PauliX(1))
>>> exp_op.decomposition()
[IsingXX((2+0j), wires=[0, 1])]


If the Hamiltonian is a Pauli word, then the decomposition is provided as a qml.PauliRot operation:

>>> qml.evolve(qml.PauliZ(0) @ qml.PauliX(1)).decomposition()
[PauliRot((2+0j), ZX, wires=[0, 1])]


Otherwise, the Hamiltonian is a linear combination of operators and the Suzuki-Trotter decomposition is used:

>>> qml.evolve(qml.sum(qml.PauliX(0), qml.PauliY(0), qml.PauliZ(0)), num_steps=2).decomposition()
[RX((1+0j), wires=[0]),
RY((1+0j), wires=[0]),
RZ((1+0j), wires=[0]),
RX((1+0j), wires=[0]),
RY((1+0j), wires=[0]),
RZ((1+0j), wires=[0])]


#### Tools for quantum chemistry and other applications 🛠️

• A new method called qml.qchem.givens_decomposition has been added, which decomposes a unitary into a sequence of Givens rotation gates with phase shifts and a diagonal phase matrix. (#3573)

unitary = np.array([[ 0.73678+0.27511j, -0.5095 +0.10704j, -0.06847+0.32515j],
[-0.21271+0.34938j, -0.38853+0.36497j,  0.61467-0.41317j],
[ 0.41356-0.20765j, -0.00651-0.66689j,  0.32839-0.48293j]])

phase_mat, ordered_rotations = qml.qchem.givens_decomposition(unitary)

>>> phase_mat
tensor([-0.20604358+0.9785369j , -0.82993272+0.55786114j,
>>> ordered_rotations
[(tensor([[-0.65087861-0.63937521j, -0.40933651-0.j        ],
(0, 1)),
(tensor([[ 0.47970366-0.33308926j, -0.8117487 -0.j        ],
[ 0.66677093-0.46298215j,  0.5840069 -0.j        ]], requires_grad=True),
(1, 2)),
(tensor([[ 0.36147547+0.73779454j, -0.57008306-0.j        ],
[ 0.2508207 +0.51194108j,  0.82158706-0.j        ]], requires_grad=True),
(0, 1))]

• A new template called qml.BasisRotation has been added, which performs a basis transformation defined by a set of fermionic ladder operators. (#3573)

import pennylane as qml
from pennylane import numpy as np

V = np.array([[ 0.53672126+0.j        , -0.1126064 -2.41479668j],
[-0.1126064 +2.41479668j,  1.48694623+0.j        ]])
eigen_vals, eigen_vecs = np.linalg.eigh(V)
umat = eigen_vecs.T
wires = range(len(umat))
def circuit():
for idx, eigenval in enumerate(eigen_vals):
qml.RZ(eigenval, wires=[idx])
qml.BasisRotation(wires=wires, unitary_matrix=umat)

>>> circ_unitary = qml.matrix(circuit)()
>>> np.round(circ_unitary/circ_unitary[0][0], 3)
tensor([[ 1.   -0.j   , -0.   +0.j   , -0.   +0.j   , -0.   +0.j   ],
[-0.   +0.j   , -0.516-0.596j, -0.302-0.536j, -0.   +0.j   ],
[-0.   +0.j   ,  0.35 +0.506j, -0.311-0.724j, -0.   +0.j   ],
[-0.   +0.j   , -0.   +0.j   , -0.   +0.j   , -0.438+0.899j]], requires_grad=True)

• A new function called qml.qchem.load_basisset has been added to extract qml.qchem basis set data from the Basis Set Exchange library. (#3363)

• A new function called qml.math.max_entropy has been added to compute the maximum entropy of a quantum state. (#3594)

• A new template called qml.TwoLocalSwapNetwork has been added that implements a canonical 2-complete linear (2-CCL) swap network described in arXiv:1905.05118. (#3447)

dev = qml.device('default.qubit', wires=5)
weights = np.random.random(size=qml.templates.TwoLocalSwapNetwork.shape(len(dev.wires)))
acquaintances = lambda index, wires, param: (qml.CRY(param, wires=index)
if np.abs(wires[0]-wires[1]) else qml.CRZ(param, wires=index))
@qml.qnode(dev)
def swap_network_circuit():
qml.templates.TwoLocalSwapNetwork(dev.wires, acquaintances, weights, fermionic=False)
return qml.state()

>>> print(weights)
tensor([0.20308242, 0.91906199, 0.67988804, 0.81290256, 0.08708985,
0.81860084, 0.34448344, 0.05655892, 0.61781612, 0.51829044], requires_grad=True)
>>> print(qml.draw(swap_network_circuit, expansion_strategy = 'device')())
0: ─╭●────────╭SWAP─────────────────╭●────────╭SWAP─────────────────╭●────────╭SWAP─┤  State
1: ─╰RY(0.20)─╰SWAP─╭●────────╭SWAP─╰RY(0.09)─╰SWAP─╭●────────╭SWAP─╰RY(0.62)─╰SWAP─┤  State
2: ─╭●────────╭SWAP─╰RY(0.68)─╰SWAP─╭●────────╭SWAP─╰RY(0.34)─╰SWAP─╭●────────╭SWAP─┤  State
3: ─╰RY(0.92)─╰SWAP─╭●────────╭SWAP─╰RY(0.82)─╰SWAP─╭●────────╭SWAP─╰RY(0.52)─╰SWAP─┤  State
4: ─────────────────╰RY(0.81)─╰SWAP─────────────────╰RY(0.06)─╰SWAP─────────────────┤  State


### Improvements 🛠

#### Pulse programming

• A new function called qml.pulse.pwc has been added as a convenience function for defining a qml.pulse.ParametrizedHamiltonian. This function can be used to create a callable coefficient by setting the timespan over which the function should be non-zero. The resulting callable can be passed an array of parameters and a time. (#3645)

>>> timespan = (2, 4)
>>> f = qml.pulse.pwc(timespan)
>>> f * qml.PauliX(0)
ParametrizedHamiltonian: terms=1


The params array will be used as bin values evenly distributed over the timespan, and the parameter t will determine which of the bins is returned.

>>> f(params=[1.2, 2.3, 3.4, 4.5], t=3.9)
DeviceArray(4.5, dtype=float32)
>>> f(params=[1.2, 2.3, 3.4, 4.5], t=6)  # zero outside the range (2, 4)
DeviceArray(0., dtype=float32)

• A new function calledqml.pulse.pwc_from_function has been added as a decorator for defining a qml.pulse.ParametrizedHamiltonian. This function can be used to decorate a function and create a piecewise constant approximation of it. (#3645)

>>> @qml.pulse.pwc_from_function((2, 4), num_bins=10)
... def f1(p, t):
...     return p * t


The resulting function approximates the same of p**2 * t on the interval t=(2, 4) in 10 bins, and returns zero outside the interval.

# t=2 and t=2.1 are within the same bin
>>> f1(3, 2), f1(3, 2.1)
(DeviceArray(6., dtype=float32), DeviceArray(6., dtype=float32))
# next bin
>>> f1(3, 2.2)
DeviceArray(6.6666665, dtype=float32)
# outside the interval t=(2, 4)
>>> f1(3, 5)
DeviceArray(0., dtype=float32)

• Add ParametrizedHamiltonianPytree class, which is a pytree jax object representing a parametrized Hamiltonian, where the matrix computation is delayed to improve performance. (#3779)

#### Operations and batching

• The function qml.dot has been updated to compute the dot product between a vector and a list of operators. (#3586)

>>> coeffs = np.array([1.1, 2.2])
>>> ops = [qml.PauliX(0), qml.PauliY(0)]
>>> qml.dot(coeffs, ops)
(1.1*(PauliX(wires=[0]))) + (2.2*(PauliY(wires=[0])))
>>> qml.dot(coeffs, ops, pauli=True)
1.1 * X(0) + 2.2 * Y(0)

• qml.evolve returns the evolution of an Operator or a ParametrizedHamiltonian. (#3617) (#3706)

• qml.ControlledQubitUnitary now inherits from qml.ops.op_math.ControlledOp, which defines decomposition, expand, and sparse_matrix rather than raising an error. (#3450)

• Parameter broadcasting support has been added for the qml.ops.op_math.Controlled class if the base operator supports broadcasting. (#3450)

• The qml.generator function now checks if the generator is Hermitian, rather than whether it is a subclass of Observable. This allows it to return valid generators from SymbolicOp and CompositeOp classes. (#3485)

• The qml.equal function has been extended to compare Prod and Sum operators. (#3516)

• qml.purity has been added as a measurement process for purity (#3551)

• In-place inversion has been removed for qutrit operations in preparation for the removal of in-place inversion. (#3566)

• The qml.utils.sparse_hamiltonian function has been moved to thee qml.Hamiltonian.sparse_matrix method. (#3585)

• The qml.pauli.PauliSentence.operation() method has been improved to avoid instantiating an SProd operator when the coefficient is equal to 1. (#3595)

• Batching is now allowed in all SymbolicOp operators, which include Exp, Pow and SProd. (#3597)

• The Sum and Prod operations now have broadcasted operands. (#3611)

• The XYX single-qubit unitary decomposition has been implemented. (#3628)

• All dunder methods now return NotImplemented, allowing the right dunder method (e.g. __radd__) of the other class to be called. (#3631)

• The qml.GellMann operators now include their index when displayed. (#3641)

• qml.ops.ctrl_decomp_zyz has been added to compute the decomposition of a controlled single-qubit operation given a single-qubit operation and the control wires. (#3681)

• qml.pauli.is_pauli_word now supports Prod and SProd operators, and it returns False when a Hamiltonian contains more than one term. (#3692)

• qml.pauli.pauli_word_to_string now supports Prod, SProd and Hamiltonian operators. (#3692)

• qml.ops.op_math.Controlled can now decompose single qubit target operations more effectively using the ZYZ decomposition. (#3726)

• The qml.qchem.Molecule class raises an error when the molecule has an odd number of electrons or when the spin multiplicity is not 1. (#3748)

• qml.qchem.basis_rotation now accounts for spin, allowing it to perform Basis Rotation Groupings for molecular hamiltonians. (#3714) (#3774)

• The gradient transforms work for the new return type system with non-trivial classical jacobians. (#3776)

• The default.mixed device has received a performance improvement for multi-qubit operations. This also allows to apply channels that act on more than seven qubits, which was not possible before. (#3584)

• qml.dot now groups coefficients together. (#3691)

>>> qml.dot(coeffs=[2, 2, 2], ops=[qml.PauliX(0), qml.PauliY(1), qml.PauliZ(2)])
2*(PauliX(wires=[0]) + PauliY(wires=[1]) + PauliZ(wires=[2]))

• qml.generator now supports operators with Sum and Prod generators. (#3691)

• The Sum._sort method now takes into account the name of the operator when sorting. (#3691)

• A new tape transform called qml.transforms.sign_expand has been added. It implements the optimal decomposition of a fast-forwardable Hamiltonian that minimizes the variance of its estimator in the Single-Qubit-Measurement from arXiv:2207.09479. (#2852)

#### Differentiability and interfaces

• The qml.math module now also contains a submodule for fast Fourier transforms, qml.math.fft. (#1440)

The submodule in particular provides differentiable versions of the following functions, available in all common interfaces for PennyLane

Note that the output of the derivative of these functions may differ when used with complex-valued inputs, due to different conventions on complex-valued derivatives.

• Validation has been added on gradient keyword arguments when initializing a QNode — if unexpected keyword arguments are passed, a UserWarning is raised. A list of the current expected gradient function keyword arguments can be accessed via qml.gradients.SUPPORTED_GRADIENT_KWARGS. (#3526)

• The numpy version has been constrained to <1.24. (#3563)

• Support for two-qubit unitary decomposition with JAX-JIT has been added. (#3569)

• qml.math.size now supports PyTorch tensors. (#3606)

• Most quantum channels are now fully differentiable on all interfaces. (#3612)

• qml.math.matmul now supports PyTorch and Autograd tensors. (#3613)

• Add qml.math.detach, which detaches a tensor from its trace. This stops automatic gradient computations. (#3674)

• Add typing.TensorLike type. (#3675)

• qml.QuantumMonteCarlo template is now JAX-JIT compatible when passing jax.numpy arrays to the template. (#3734)

• DefaultQubitJax now supports evolving the state vector when executing qml.pulse.ParametrizedEvolution gates. (#3743)

• SProd.sparse_matrix now supports interface-specific variables with a single element as the scalar. (#3770)

• Added argnum argument to metric_tensor. By passing a sequence of indices referring to trainable tape parameters, the metric tensor is only computed with respect to these parameters. This reduces the number of tapes that have to be run. (#3587)

• The parameter-shift derivative of variances saves a redundant evaluation of the corresponding unshifted expectation value tape, if possible (#3744)

#### Next generation device API

• The apply_operation single-dispatch function is added to devices/qubit that applies an operation to a state and returns a new state. (#3637)

• The preprocess function is added to devices/qubit that validates, expands, and transforms a batch of QuantumTape objects to abstract preprocessing details away from the device. (#3708)

• The create_initial_state function is added to devices/qubit that returns an initial state for an execution. (#3683)

• The simulate function is added to devices/qubit that turns a single quantum tape into a measurement result. The function only supports state based measurements with either no observables or observables with diagonalizing gates. It supports simultaneous measurement of non-commuting observables. (#3700)

• The ExecutionConfig data class has been added. (#3649)

• The StatePrep class has been added as an interface that state-prep operators must implement. (#3654)

• qml.QubitStateVector now implements the StatePrep interface. (#3685)

• qml.BasisState now implements the StatePrep interface. (#3693)

• New Abstract Base Class for devices Device is added to the devices.experimental submodule. This interface is still in experimental mode and not integrated with the rest of pennylane. (#3602)

#### Other improvements

• Writing Hamiltonians to a file using the qml.data module has been improved by employing a condensed writing format. (#3592)

• Lazy-loading in the qml.data.Dataset.read() method is more universally supported. (#3605)

• The qchem.Molecule class raises an error when the molecule has an odd number of electrons or when the spin multiplicity is not 1. (#3748)

• qml.draw and qml.draw_mpl have been updated to draw any quantum function, which allows for visualizing only part of a complete circuit/QNode. (#3760)

• The string representation of a Measurement Process now includes the _eigvals property if it is set. (#3820)

### Breaking changes 💔

• The argument mode in execution has been replaced by the boolean grad_on_execution in the new execution pipeline. (#3723)

• qml.VQECost has been removed. (#3735)

• The default interface is now auto. (#3677) (#3752) (#3829)

The interface is determined during the QNode call instead of the initialization. It means that the gradient_fn and gradient_kwargs are only defined on the QNode at the beginning of the call. Moreover, without specifying the interface it is not possible to guarantee that the device will not be changed during the call if you are using backprop (such as default.qubit changing to default.qubit.jax) whereas before it was happening at initialization.

• The tape method get_operation can also now return the operation index in the tape, and it can be activated by setting the return_op_index to True: get_operation(idx, return_op_index=True). It will become the default in version 0.30. (#3667)

• Operation.inv() and the Operation.inverse setter have been removed. Please use qml.adjoint or qml.pow instead. (#3618)

>>> qml.PauliX(0).inv()


use

>>> qml.adjoint(qml.PauliX(0))

• The Operation.inverse property has been removed completely. (#3725)

• The target wires of qml.ControlledQubitUnitary are no longer available via op.hyperparameters["u_wires"]. Instead, they can be accesses via op.base.wires or op.target_wires. (#3450)

• The tape constructed by a QNode is no longer queued to surrounding contexts. (#3509)

• Nested operators like Tensor, Hamiltonian, and Adjoint now remove their owned operators from the queue instead of updating their metadata to have an "owner". (#3282)

• qml.qchem.scf, qml.RandomLayers.compute_decomposition, and qml.Wires.select_random now use local random number generators instead of global random number generators. This may lead to slightly different random numbers and an independence of the results from the global random number generation state. Please provide a seed to each individual function instead if you want controllable results. (#3624)

• qml.transforms.measurement_grouping has been removed. Users should use qml.transforms.hamiltonian_expand instead. (#3701)

• op.simplify() for operators which are linear combinations of Pauli words will use a builtin Pauli representation to more efficiently compute the simplification of the operator. (#3481)

• All Operator‘s input parameters that are lists are cast into vanilla numpy arrays. (#3659)

• QubitDevice.expval no longer permutes an observable’s wire order before passing it to QubitDevice.probability. The associated downstream changes for default.qubit have been made, but this may still affect expectations for other devices that inherit from QubitDevice and override probability (or any other helper functions that take a wire order such as marginal_prob, estimate_probability or analytic_probability). (#3753)

### Deprecations 👋

• qml.utils.sparse_hamiltonian function has been deprecated, and usage will now raise a warning. Instead, one should use the qml.Hamiltonian.sparse_matrix method. (#3585)

• The collections module has been deprecated. (#3686) (#3687)

• qml.op_sum has been deprecated. Users should use qml.sum instead. (#3686)

• The use of Evolution directly has been deprecated. Users should use qml.evolve instead. This new function changes the sign of the given parameter. (#3706)

• Use of qml.dot with a QNodeCollection has been deprecated. (#3586)

### Documentation 📝

• Revise note on GPU support in the circuit introduction. (#3836)

• Make warning about vanilla version of NumPy for differentiation more prominent. (#3838)

• The documentation for qml.operation has been improved. (#3664)

• The code example in qml.SparseHamiltonian has been updated with the correct wire range. (#3643)

• A hyperlink has been added in the text for a URL in the qml.qchem.mol_data docstring. (#3644)

• A typo was corrected in the documentation for qml.math.vn_entropy. (#3740)

### Bug fixes 🐛

• Fixed a bug where measuring qml.probs in the computational basis with non-commuting measurements returned incorrect results. Now an error is raised. (#3811)

• Fixed a bug where measuring qml.probs in the computational basis with non-commuting measurements returned incorrect results. Now an error is raised. (#3811)

• Fixed a bug in the drawer where nested controlled operations would output the label of the operation being controlled, rather than the control values. (#3745)

• Fixed a bug in qml.transforms.metric_tensor where prefactors of operation generators were taken into account multiple times, leading to wrong outputs for non-standard operations. (#3579)

• Local random number generators are now used where possible to avoid mutating the global random state. (#3624)

• The networkx version change being broken has been fixed by selectively skipping a qcut TensorFlow-JIT test. (#3609) (#3619)

• Fixed the wires for the Y decomposition in the ZX calculus transform. (#3598)

• qml.pauli.PauliWord is now pickle-able. (#3588)

• Child classes of QuantumScript now return their own type when using SomeChildClass.from_queue. (#3501)

• A typo has been fixed in the calculation and error messages in operation.py (#3536)

• qml.data.Dataset.write() now ensures that any lazy-loaded values are loaded before they are written to a file. (#3605)

• Tensor._batch_size is now set to None during initialization, copying and map_wires. (#3642) (#3661)

• Tensor.has_matrix is now set to True. (#3647)

• Fixed typo in the example of qml.IsingZZ gate decomposition. (#3676)

• Fixed a bug that made tapes/qnodes using qml.Snapshot incompatible with qml.drawer.tape_mpl. (#3704)

• Tensor._pauli_rep is set to None during initialization and Tensor.data has been added to its setter. (#3722)

• qml.math.ndim has been redirected to jnp.ndim when using it on a jax tensor. (#3730)

• Implementations of marginal_prob (and subsequently, qml.probs) now return probabilities with the expected wire order. (#3753)

This bug affected most probabilistic measurement processes on devices that inherit from QubitDevice when the measured wires are out of order with respect to the device wires and 3 or more wires are measured. The assumption was that marginal probabilities would be computed with the device’s state and wire order, then re-ordered according to the measurement process wire order. Instead, the re-ordering went in the inverse direction (that is, from measurement process wire order to device wire order). This is now fixed. Note that this only occurred for 3 or more measured wires because this mapping is identical otherwise. More details and discussion of this bug can be found in the original bug report.

• Empty iterables can no longer be returned from QNodes. (#3769)

• The keyword arguments for qml.equal now are used when comparing the observables of a Measurement Process. The eigvals of measurements are only requested if both observables are None, saving computational effort. (#3820)

• Only converts input to qml.Hermitian to a numpy array if the input is a list. (#3820)

### Contributors ✍

This release contains contributions from (in alphabetical order):

Gian-Luca Anselmetti, Guillermo Alonso-Linaje, Juan Miguel Arrazola, Ikko Ashimine, Utkarsh Azad, Miriam Beddig, Cristian Boghiu, Thomas Bromley, Astral Cai, Isaac De Vlugt, Olivia Di Matteo, Lillian M. A. Frederiksen, Soran Jahangiri, Korbinian Kottmann, Christina Lee, Albert Mitjans Coma, Romain Moyard, Mudit Pandey, Borja Requena, Matthew Silverman, Jay Soni, Antal Száva, Frederik Wilde, David Wierichs, Moritz Willmann.

orphan

## Release 0.28.0¶

### New features since last release

#### Custom measurement processes 📐

• Custom measurements can now be facilitated with the addition of the qml.measurements module. (#3286) (#3343) (#3288) (#3312) (#3287) (#3292) (#3287) (#3326) (#3327) (#3388) (#3439) (#3466)

Within qml.measurements are new subclasses that allow for the possibility to create custom measurements:

• SampleMeasurement: represents a sample-based measurement

• StateMeasurement: represents a state-based measurement

• MeasurementTransform: represents a measurement process that requires the application of a batch transform

Creating a custom measurement involves making a class that inherits from one of the classes above. An example is given below. Here, the measurement computes the number of samples obtained of a given state:

from pennylane.measurements import SampleMeasurement

class CountState(SampleMeasurement):
def __init__(self, state: str):
self.state = state  # string identifying the state, e.g. "0101"
wires = list(range(len(state)))
super().__init__(wires=wires)

def process_samples(self, samples, wire_order, shot_range, bin_size):
counts_mp = qml.counts(wires=self._wires)
counts = counts_mp.process_samples(samples, wire_order, shot_range, bin_size)
return counts.get(self.state, 0)

def __copy__(self):
return CountState(state=self.state)


We can now execute the new measurement in a QNode as follows.

dev = qml.device("default.qubit", wires=1, shots=10000)

@qml.qnode(dev)
def circuit(x):
qml.RX(x, wires=0)
return CountState(state="1")

>>> circuit(1.23)


Differentiability is also supported for this new measurement process:

>>> x = qml.numpy.array(1.23, requires_grad=True)
4715.000000000001


For more information about these new features, see the documentation for qml.measurements <https://docs.pennylane.ai/en/stable/code/qml_measurements.html>_.

#### ZX Calculus 🧮

• QNodes can now be converted into ZX diagrams via the PyZX framework. (#3446)

ZX diagrams are the medium for which we can envision a quantum circuit as a graph in the ZX-calculus language, showing properties of quantum protocols in a visually compact and logically complete fashion.

QNodes decorated with @qml.transforms.to_zx will return a PyZX graph that represents the computation in the ZX-calculus language.

dev = qml.device("default.qubit", wires=2)

@qml.transforms.to_zx
@qml.qnode(device=dev)
def circuit(p):
qml.RZ(p[0], wires=1),
qml.RZ(p[1], wires=1),
qml.RX(p[2], wires=0),
qml.PauliZ(wires=0),
qml.RZ(p[3], wires=1),
qml.PauliX(wires=1),
qml.CNOT(wires=[0, 1]),
qml.CNOT(wires=[1, 0]),
qml.SWAP(wires=[0, 1]),
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

>>> params = [5 / 4 * np.pi, 3 / 4 * np.pi, 0.1, 0.3]
>>> circuit(params)
Graph(20 vertices, 23 edges)


Information about PyZX graphs can be found in the PyZX Graphs API.

#### QChem databases and basis sets ⚛️

• The symbols and geometry of a compound from the PubChem database can now be accessed via qchem.mol_data(). (#3289) (#3378)

>>> import pennylane as qml
>>> from pennylane.qchem import mol_data
>>> mol_data("BeH2")
(['Be', 'H', 'H'],
tensor([[ 4.79404621,  0.29290755,  0.        ],
[ 3.77945225, -0.29290755,  0.        ],
[ 5.80882913, -0.29290755,  0.        ]], requires_grad=True))
>>> mol_data(223, "CID")
(['N', 'H', 'H', 'H', 'H'],
tensor([[ 0.        ,  0.        ,  0.        ],
[ 1.82264085,  0.52836742,  0.40402345],
[ 0.01417295, -1.67429735, -0.98038991],
[-0.98927163, -0.22714508,  1.65369933],

• Perform quantum chemistry calculations with two new basis sets: 6-311g and CC-PVDZ. (#3279)

>>> symbols = ["H", "He"]
>>> geometry = np.array([[1.0, 0.0, 0.0], [0.0, 0.0, 0.0]], requires_grad=False)
>>> charge = 1
>>> basis_names = ["6-311G", "CC-PVDZ"]
>>> for basis_name in basis_names:
...     mol = qml.qchem.Molecule(symbols, geometry, charge=charge, basis_name=basis_name)
...     print(qml.qchem.hf_energy(mol)())
[-2.84429531]
[-2.84061284]


#### A bunch of new operators 👀

• The controlled CZ gate and controlled Hadamard gate are now available via qml.CCZ and qml.CH, respectively. (#3408)

>>> ccz = qml.CCZ(wires=[0, 1, 2])
>>> qml.matrix(ccz)
[[ 1  0  0  0  0  0  0  0]
[ 0  1  0  0  0  0  0  0]
[ 0  0  1  0  0  0  0  0]
[ 0  0  0  1  0  0  0  0]
[ 0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  1  0  0]
[ 0  0  0  0  0  0  1  0]
[ 0  0  0  0  0  0  0 -1]]
>>> ch = qml.CH(wires=[0, 1])
>>> qml.matrix(ch)
[[ 1.          0.          0.          0.        ]
[ 0.          1.          0.          0.        ]
[ 0.          0.          0.70710678  0.70710678]
[ 0.          0.          0.70710678 -0.70710678]]

• Three new parametric operators, qml.CPhaseShift00, qml.CPhaseShift01, and qml.CPhaseShift10, are now available. Each of these operators performs a phase shift akin to qml.ControlledPhaseShift but on different positions of the state vector. (#2715)

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
>>> def circuit():
...     qml.PauliX(wires=1)
...     qml.CPhaseShift01(phi=1.23, wires=[0,1])
...     return qml.state()
...
>>> circuit()
tensor([0.        +0.j       , 0.33423773+0.9424888j,
1.        +0.j       , 0.        +0.j       ], requires_grad=True)

• A new gate operation called qml.FermionicSWAP has been added. This implements the exchange of spin orbitals representing fermionic-modes while maintaining proper anti-symmetrization. (#3380)

dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(phi):
qml.BasisState(np.array([0, 1]), wires=[0, 1])
qml.FermionicSWAP(phi, wires=[0, 1])
return qml.state()

>>> circuit(0.1)
tensor([0.        +0.j        , 0.99750208+0.04991671j,

• Create operators defined from a generator via qml.ops.op_math.Evolution. (#3375)

qml.ops.op_math.Evolution defines the exponential of an operator $hat{O}$ of the form $e^{ixhat{O}}$, with a single trainable parameter, $x$. Limiting to a single trainable parameter allows the use of qml.gradients.param_shift to find the gradient with respect to the parameter $x$.

dev = qml.device('default.qubit', wires=2)

def circuit(phi):
qml.ops.op_math.Evolution(qml.PauliX(0), -.5 * phi)
return qml.expval(qml.PauliZ(0))

>>> phi = np.array(1.2)
>>> circuit(phi)
-0.9320390495504149

• The qutrit Hadamard gate, qml.THadamard, is now available. (#3340)

The operation accepts a subspace keyword argument which determines which variant of the qutrit Hadamard to use.

>>> th = qml.THadamard(wires=0, subspace=[0, 1])
>>> qml.matrix(th)
array([[ 0.70710678+0.j,  0.70710678+0.j,  0.        +0.j],
[ 0.70710678+0.j, -0.70710678+0.j,  0.        +0.j],
[ 0.        +0.j,  0.        +0.j,  1.        +0.j]])


#### New transforms, functions, and more 😯

• Calculating the purity of arbitrary quantum states is now supported. (#3290)

The purity can be calculated in an analogous fashion to, say, the Von Neumann entropy:

• qml.math.purity can be used as an in-line function:

>>> x = [1, 0, 0, 1] / np.sqrt(2)
>>> qml.math.purity(x, [0, 1])
1.0
>>> qml.math.purity(x, [0])
0.5

>>> x = [[1 / 2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1 / 2]]
>>> qml.math.purity(x, [0, 1])
0.5

• qml.qinfo.transforms.purity can transform a QNode returning a state to a function that returns the purity:

dev = qml.device("default.mixed", wires=2)

@qml.qnode(dev)
def circuit(x):
qml.IsingXX(x, wires=[0, 1])
return qml.state()

>>> qml.qinfo.transforms.purity(circuit, wires=[0])(np.pi / 2)
0.5
>>> qml.qinfo.transforms.purity(circuit, wires=[0, 1])(np.pi / 2)
1.0


As with the other methods in qml.qinfo, the purity is fully differentiable:

>>> param = np.array(np.pi / 4, requires_grad=True)
-0.5

• A new gradient transform, qml.gradients.spsa_grad, that is based on the idea of SPSA is now available. (#3366)

This new transform allows users to compute a single estimate of a quantum gradient using simultaneous perturbation of parameters and a stochastic approximation. A QNode that takes, say, an argument x, the approximate gradient can be computed as follows.

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit(x):
...     qml.RX(x, 0)
...     qml.RX(x, 1)
...     return qml.expval(qml.PauliZ(0))
array(-0.38876964)


The argument num_directions determines how many directions of simultaneous perturbation are used, which is proportional to the number of circuit evaluations. See the SPSA gradient transform documentation for details. Note that the full SPSA optimizer is already available as qml.SPSAOptimizer.

• Multiple mid-circuit measurements can now be combined arithmetically to create new conditionals. (#3159)

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev)
def circuit():
m0 = qml.measure(wires=0)
m1 = qml.measure(wires=1)
combined = 2 * m1 + m0
qml.cond(combined == 2, qml.RX)(1.3, wires=2)
return qml.probs(wires=2)

>>> circuit()
[0.90843735 0.09156265]

• A new method called pauli_decompose() has been added to the qml.pauli module, which takes a hermitian matrix, decomposes it in the Pauli basis, and returns it either as a qml.Hamiltonian or qml.PauliSentence instance. (#3384)

• Operation or Hamiltonian instances can now be generated from a qml.PauliSentence or qml.PauliWord via the new operation() and hamiltonian() methods. (#3391)

• A sum_expand function has been added for tapes, which splits a tape measuring a Sum expectation into mutliple tapes of summand expectations, and provides a function to recombine the results. (#3230)

#### (Experimental) More interface support for multi-measurement and gradient output types 🧪

• The autograd and Tensorflow interfaces now support devices with shot vectors when qml.enable_return() has been called. (#3374) (#3400)

Here is an example using Tensorflow:

import tensorflow as tf
qml.enable_return()

dev = qml.device("default.qubit", wires=2, shots=[1000, 2000, 3000])

@qml.qnode(dev, diff_method="parameter-shift", interface="tf")
def circuit(a):
qml.RY(a, wires=0)
qml.RX(0.2, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.probs([0, 1])

>>> a = tf.Variable(0.4)
...     res = circuit(a)
...     res = tf.stack([tf.experimental.numpy.hstack(r) for r in res])
...
>>> res
<tf.Tensor: shape=(3, 5), dtype=float64, numpy=
array([[0.902, 0.951, 0.   , 0.   , 0.049],
[0.898, 0.949, 0.   , 0.   , 0.051],
[0.892, 0.946, 0.   , 0.   , 0.054]])>
>>> tape.jacobian(res, a)
<tf.Tensor: shape=(3, 5), dtype=float64, numpy=
array([[-0.345     , -0.1725    ,  0.        ,  0.        ,  0.1725    ],
[-0.383     , -0.1915    ,  0.        ,  0.        ,  0.1915    ],
[-0.38466667, -0.19233333,  0.        ,  0.        ,  0.19233333]])>

• The PyTorch interface is now fully supported when qml.enable_return() has been called, allowing the calculation of the Jacobian and the Hessian using custom differentiation methods (e.g., parameter-shift, finite difference, or adjoint). (#3416)

import torch

qml.enable_return()

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev, diff_method="parameter-shift", interface="torch")
def circuit(a, b):
qml.RY(a, wires=0)
qml.RX(b, wires=1)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.probs([0, 1])

>>> a = torch.tensor(0.1, requires_grad=True)
((tensor(-0.0998), tensor(0.)), (tensor([-0.0494, -0.0005,  0.0005,  0.0494]), tensor([-0.0991,  0.0991,  0.0002, -0.0002])))

• The JAX-JIT interface now supports first-order gradient computation when qml.enable_return() has been called. (#3235) (#3445)

import jax
from jax import numpy as jnp

jax.config.update("jax_enable_x64", True)

qml.enable_return()

dev = qml.device("lightning.qubit", wires=2)

@jax.jit
@qml.qnode(dev, interface="jax-jit", diff_method="parameter-shift")
def circuit(a, b):
qml.RY(a, wires=0)
qml.RX(b, wires=0)
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))

a, b = jnp.array(1.0), jnp.array(2.0)

>>> jax.jacobian(circuit, argnums=[0, 1])(a, b)
((Array(0.35017549, dtype=float64, weak_type=True),
Array(-0.4912955, dtype=float64, weak_type=True)),
(Array(5.55111512e-17, dtype=float64, weak_type=True),
Array(0., dtype=float64, weak_type=True)))


### Improvements 🛠

• qml.pauli.is_pauli_word now supports instances of qml.Hamiltonian. (#3389)

• When qml.probs, qml.counts, and qml.sample are called with no arguments, they measure all wires. Calling any of the aforementioned measurements with an empty wire list (e.g., qml.sample(wires=[])) will raise an error. (#3299)

• Made qml.gradients.finite_diff more convenient to use with custom data type observables/devices by reducing the number of magic methods that need to be defined in the custom data type to support finite_diff. (#3426)

• The qml.ISWAP gate is now natively supported on default.mixed, improving on its efficiency. (#3284)

• Added more input validation to qml.transforms.hamiltonian_expand such that Hamiltonian objects with no terms raise an error. (#3339)

• Continuous integration checks are now performed for Python 3.11 and Torch v1.13. Python 3.7 is dropped. (#3276)

• qml.Tracker now also logs results in tracker.history when tracking the execution of a circuit.

(#3306)

• The execution time of Wires.all_wires has been improved by avoiding data type changes and making use of itertools.chain. (#3302)

• Printing an instance of qml.qchem.Molecule is now more concise and informational. (#3364)

• The error message for qml.transforms.insert when it fails to diagonalize non-qubit-wise-commuting observables is now more detailed. (#3381)

• Extended the qml.equal function to qml.Hamiltonian and Tensor objects. (#3390)

• QuantumTape._process_queue has been moved to qml.queuing.process_queue to disentangle its functionality from the QuantumTape class. (#3401)

• QPE can now accept a target operator instead of a matrix and target wires pair. (#3373)

• The qml.ops.op_math.Controlled.map_wires method now uses base.map_wires internally instead of the private _wires property setter. (#3405)

• A new function called qml.tape.make_qscript has been created for converting a quantum function into a quantum script. This replaces qml.transforms.make_tape. (#3429)

• Add a _pauli_rep attribute to operators to integrate the new Pauli arithmetic classes with native PennyLane objects. (#3443)

• Extended the functionality of qml.matrix to qutrits. (#3508)

• The qcut.py file in pennylane/transforms/ has been reorganized into multiple files that are now in pennylane/transforms/qcut/. (#3413)

• A warning now appears when creating a Tensor object with overlapping wires, informing that this can lead to undefined behaviour. (#3459)

• Extended the qml.equal function to qml.ops.op_math.Controlled and qml.ops.op_math.ControlledOp objects. (#3463)

• Nearly every instance of with QuantumTape() has been replaced with QuantumScript construction. (#3454)

• Added validate_subspace static method to qml.Operator to check the validity of the subspace of certain qutrit operations. (#3340)

• qml.equal now supports operators created via qml.s_prod, qml.pow, qml.exp, and qml.adjoint. (#3471)

• Devices can now disregard observable grouping indices in Hamiltonians through the optional use_grouping attribute. (#3456)

• Add the optional argument lazy=True to functions qml.s_prod, qml.prod and qml.op_sum to allow simplification. (#3483)

• Updated the qml.transforms.zyz_decomposition function such that it now supports broadcast operators. This means that single-qubit qml.QubitUnitary operators, instantiated from a batch of unitaries, can now be decomposed. (#3477)

• The performance of executing circuits under the jax.vmap transformation has been improved by being able to leverage the batch-execution capabilities of some devices. (#3452)

• The tolerance for converting openfermion Hamiltonian complex coefficients to real ones has been modified to prevent conversion errors. (#3367)

• OperationRecorder now inherits from AnnotatedQueue and QuantumScript instead of QuantumTape. (#3496)

• Updated qml.transforms.split_non_commuting to support the new return types. (#3414)

• Updated qml.transforms.mitigate_with_zne to support the new return types. (#3415)

• Updated qml.transforms.metric_tensor, qml.transforms.adjoint_metric_tensor, qml.qinfo.classical_fisher, and qml.qinfo.quantum_fisher to support the new return types. (#3449)

• Updated qml.transforms.batch_params and qml.transforms.batch_input to support the new return types. (#3431)

• Updated qml.transforms.cut_circuit and qml.transforms.cut_circuit_mc to support the new return types. (#3346)

• Limit NumPy version to <1.24. (#3346)

### Breaking changes 💔

• Python 3.7 support is no longer maintained. PennyLane will be maintained for versions 3.8 and up. (#3276)

• The log_base attribute has been moved from MeasurementProcess to the new VnEntropyMP and MutualInfoMP classes, which inherit from MeasurementProcess. (#3326)

• qml.utils.decompose_hamiltonian() has been removed. Please use qml.pauli.pauli_decompose() instead. (#3384)

• The return_type attribute of MeasurementProcess has been removed where possible. Use isinstance checks instead. (#3399)

• Instead of having an OrderedDict attribute called _queue, AnnotatedQueue now inherits from OrderedDict and encapsulates the queue. Consequentially, this also applies to the QuantumTape class which inherits from AnnotatedQueue. (#3401)

• The ShadowMeasurementProcess class has been renamed to ClassicalShadowMP. (#3388)

• The qml.Operation.get_parameter_shift method has been removed. The gradients module should be used for general parameter-shift rules instead. (#3419)

• The signature of the QubitDevice.statistics method has been changed from

def statistics(self, observables, shot_range=None, bin_size=None, circuit=None):


to

def statistics(self, circuit: QuantumTape, shot_range=None, bin_size=None):


(#3421)

• The MeasurementProcess class is now an abstract class and return_type is now a property of the class. (#3434)

### Deprecations 👋

Deprecations cycles are tracked at doc/developement/deprecations.rst.

• The following methods are deprecated: (#3281)

• qml.tape.get_active_tape: Use qml.QueuingManager.active_context() instead

• qml.transforms.qcut.remap_tape_wires: Use qml.map_wires instead

• qml.tape.QuantumTape.inv(): Use qml.tape.QuantumTape.adjoint() instead

• qml.tape.stop_recording(): Use qml.QueuingManager.stop_recording() instead

• qml.tape.QuantumTape.stop_recording(): Use qml.QueuingManager.stop_recording() instead

• qml.QueuingContext is now qml.QueuingManager

• QueuingManager.safe_update_info and AnnotatedQueue.safe_update_info: Use update_info instead.

• qml.transforms.measurement_grouping has been deprecated. Use qml.transforms.hamiltonian_expand instead. (#3417)

• The observables argument in QubitDevice.statistics is deprecated. Please use circuit instead. (#3433)

• The seed_recipes argument in qml.classical_shadow and qml.shadow_expval is deprecated. A new argument seed has been added, which defaults to None and can contain an integer with the wanted seed. (#3388)

• qml.transforms.make_tape has been deprecated. Please use qml.tape.make_qscript instead. (#3478)

### Documentation 📝

• Added documentation on parameter broadcasting regarding both its usage and technical aspects. (#3356)

The quickstart guide on circuits as well as the the documentation of QNodes and Operators now contain introductions and details on parameter broadcasting. The QNode documentation mostly contains usage details, the Operator documentation is concerned with implementation details and a guide to support broadcasting in custom operators.

• The return type statements of gradient and Hessian transforms and a series of other functions that are a batch_transform have been corrected. (#3476)

• Developer documentation for the queuing module has been added. (#3268)

• More mentions of diagonalizing gates for all relevant operations have been corrected. (#3409)

The docstrings for compute_eigvals used to say that the diagonalizing gates implemented $U$, the unitary such that $O = U Sigma U^{dagger}$, where $O$ is the original observable and $Sigma$ a diagonal matrix. However, the diagonalizing gates actually implement $U^{dagger}$, since $langle psi | O | psi rangle = langle psi | U Sigma U^{dagger} | psi rangle$, making $U^{dagger} | psi rangle$ the actual state being measured in the $Z$-basis.

• A warning about using dill to pickle and unpickle datasets has been added. (#3505)

### Bug fixes 🐛

• Fixed a bug that prevented qml.gradients.param_shift from being used for broadcasted tapes. (#3528)

• Fixed a bug where qml.transforms.hamiltonian_expand didn’t preserve the type of the input results in its output. (#3339)

• Fixed a bug that made qml.gradients.param_shift raise an error when used with unshifted terms only in a custom recipe, and when using any unshifted terms at all under the new return type system. (#3177)

• The original tape _obs_sharing_wires attribute is updated during its expansion. (#3293)

• An issue with drain=False in the adaptive optimizer has been fixed. Before the fix, the operator pool needed to be reconstructed inside the optimization pool when drain=False. With this fix, this reconstruction is no longer needed. (#3361)

• If the device originally has no shots but finite shots are dynamically specified, Hamiltonian expansion now occurs. (#3369)

• qml.matrix(op) now fails if the operator truly has no matrix (e.g., qml.Barrier) to match op.matrix(). (#3386)

• The pad_with argument in the qml.AmplitudeEmbedding template is now compatible with all interfaces. (#3392)

• Operator.pow now queues its constituents by default. (#3373)

• Fixed a bug where a QNode returning qml.sample would produce incorrect results when run on a device defined with a shot vector. (#3422)

• The qml.data module now works as expected on Windows. (#3504)

### Contributors ✍️

This release contains contributions from (in alphabetical order):

Guillermo Alonso, Juan Miguel Arrazola, Utkarsh Azad, Samuel Banning, Thomas Bromley, Astral Cai, Albert Mitjans Coma, Ahmed Darwish, Isaac De Vlugt, Olivia Di Matteo, Amintor Dusko, Pieter Eendebak, Lillian M. A. Frederiksen, Diego Guala, Katharine Hyatt, Josh Izaac, Soran Jahangiri, Edward Jiang, Korbinian Kottmann, Christina Lee, Romain Moyard, Lee James O’Riordan, Mudit Pandey, Kevin Shen, Matthew Silverman, Jay Soni, Antal Száva, David Wierichs, Moritz Willmann, and Filippo Vicentini.

orphan

## Release 0.27.0¶

### New features since last release

#### An all-new data module 💾

• The qml.data module is now available, allowing users to download, load, and create quantum datasets. (#3156)

Datasets are hosted on Xanadu Cloud and can be downloaded by using qml.data.load():

>>> H2_datasets = qml.data.load(
...   data_name="qchem", molname="H2", basis="STO-3G", bondlength=1.1
... )
>>> H2data = H2_datasets[0]
>>> H2data
<Dataset = description: qchem/H2/STO-3G/1.1, attributes: ['molecule', 'hamiltonian', ...]>

• Datasets available to be downloaded can be listed with qml.data.list_datasets().

• To download or load only specific properties of a dataset, we can specify the desired properties in qml.data.load with the attributes keyword argument:

>>> H2_hamiltonian = qml.data.load(
... data_name="qchem", molname="H2", basis="STO-3G", bondlength=1.1,
... attributes=["molecule", "hamiltonian"]
... )[0]
>>> H2_hamiltonian.hamiltonian
<Hamiltonian: terms=15, wires=[0, 1, 2, 3]>


The available attributes can be found using qml.data.list_attributes():

• To select data interactively, we can use qml.data.load_interactive():

>>> qml.data.load_interactive()
1) qspin
2) qchem
Choice [1-2]: 1
...
...
...
...
...

dataset: qspin/Ising/open/rectangular/4x4
attributes: ['parameters', 'ground_states']
force: False
dest folder: datasets
Would you like to continue? (Default is yes) [Y/n]:
<Dataset = description: qspin/Ising/open/rectangular/4x4, attributes: ['parameters', 'ground_states']>

• Once a dataset is loaded, its properties can be accessed as follows:

>>> dev = qml.device("default.qubit",wires=4)
>>> @qml.qnode(dev)
... def circuit():
...     qml.BasisState(H2data.hf_state, wires = [0, 1, 2, 3])
...     for op in H2data.vqe_gates:
...          qml.apply(op)
...     return qml.expval(H2data.hamiltonian)
>>> print(circuit())
-1.0791430411076344


It’s also possible to create custom datasets with qml.data.Dataset:

>>> example_hamiltonian = qml.Hamiltonian(coeffs=[1,0.5], observables=[qml.PauliZ(wires=0),qml.PauliX(wires=1)])
>>> example_energies, _ = np.linalg.eigh(qml.matrix(example_hamiltonian))
>>> example_dataset = qml.data.Dataset(
... data_name = 'Example', hamiltonian=example_hamiltonian, energies=example_energies
... )
>>> example_dataset.data_name
'Example'
>>> example_dataset.hamiltonian
(0.5) [X1]
+ (1) [Z0]
>>> example_dataset.energies
array([-1.5, -0.5,  0.5,  1.5])


Custom datasets can be saved and read with the qml.data.Dataset.write() and qml.data.Dataset.read() methods, respectively.

>>> example_dataset.write('./path/to/dataset.dat')
'Example'
(0.5) [X1]
+ (1) [Z0]
array([-1.5, -0.5,  0.5,  1.5])


We will continue to work on adding more datasets and features for qml.data in future releases.

• Optimizing quantum circuits can now be done adaptively with qml.AdaptiveOptimizer. (#3192)

The qml.AdaptiveOptimizer takes an initial circuit and a collection of operators as input and adds a selected gate to the circuit at each optimization step. The process of growing the circuit can be repeated until the circuit gradients converge to zero within a given threshold. The adaptive optimizer can be used to implement algorithms such as ADAPT-VQE as shown in the following example.

Firstly, we define some preliminary variables needed for VQE:

symbols = ["H", "H", "H"]
geometry = np.array([[0.01076341, 0.04449877, 0.0],
[0.98729513, 1.63059094, 0.0],
H, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry, charge = 1)


The collection of gates to grow the circuit is built to contain all single and double excitations:

n_electrons = 2
singles, doubles = qml.qchem.excitations(n_electrons, qubits)
singles_excitations = [qml.SingleExcitation(0.0, x) for x in singles]
doubles_excitations = [qml.DoubleExcitation(0.0, x) for x in doubles]
operator_pool = doubles_excitations + singles_excitations


Next, an initial circuit that prepares a Hartree-Fock state and returns the expectation value of the Hamiltonian is defined:

hf_state = qml.qchem.hf_state(n_electrons, qubits)
dev = qml.device("default.qubit", wires=qubits)
@qml.qnode(dev)
def circuit():
qml.BasisState(hf_state, wires=range(qubits))
return qml.expval(H)


Finally, the optimizer is instantiated and then the circuit is created and optimized adaptively:

opt = qml.optimize.AdaptiveOptimizer()
for i in range(len(operator_pool)):
circuit, energy, gradient = opt.step_and_cost(circuit, operator_pool, drain_pool=True)
print('Energy:', energy)
print(qml.draw(circuit)())
print()
break

Energy: -1.246549938420637
0: ─╭BasisState(M0)─╭G²(0.20)─┤ ╭<𝓗>
1: ─├BasisState(M0)─├G²(0.20)─┤ ├<𝓗>
2: ─├BasisState(M0)─│─────────┤ ├<𝓗>
3: ─├BasisState(M0)─│─────────┤ ├<𝓗>
4: ─├BasisState(M0)─├G²(0.20)─┤ ├<𝓗>
5: ─╰BasisState(M0)─╰G²(0.20)─┤ ╰<𝓗>

Energy: -1.2613740231529604
0: ─╭BasisState(M0)─╭G²(0.20)─╭G²(0.19)─┤ ╭<𝓗>
1: ─├BasisState(M0)─├G²(0.20)─├G²(0.19)─┤ ├<𝓗>
2: ─├BasisState(M0)─│─────────├G²(0.19)─┤ ├<𝓗>
3: ─├BasisState(M0)─│─────────╰G²(0.19)─┤ ├<𝓗>
4: ─├BasisState(M0)─├G²(0.20)───────────┤ ├<𝓗>
5: ─╰BasisState(M0)─╰G²(0.20)───────────┤ ╰<𝓗>

Energy: -1.2743971719780331
0: ─╭BasisState(M0)─╭G²(0.20)─╭G²(0.19)──────────┤ ╭<𝓗>
1: ─├BasisState(M0)─├G²(0.20)─├G²(0.19)─╭G(0.00)─┤ ├<𝓗>
2: ─├BasisState(M0)─│─────────├G²(0.19)─│────────┤ ├<𝓗>
3: ─├BasisState(M0)─│─────────╰G²(0.19)─╰G(0.00)─┤ ├<𝓗>
4: ─├BasisState(M0)─├G²(0.20)────────────────────┤ ├<𝓗>
5: ─╰BasisState(M0)─╰G²(0.20)────────────────────┤ ╰<𝓗>


For a detailed breakdown of its implementation, check out the Adaptive circuits for quantum chemistry demo.

#### Automatic interface detection 🧩

• QNodes now accept an auto interface argument which automatically detects the machine learning library to use. (#3132)

from pennylane import numpy as np
import torch
import tensorflow as tf
from jax import numpy as jnp

dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev, interface="auto")
def circuit(weight):
qml.RX(weight[0], wires=0)
qml.RY(weight[1], wires=1)
return qml.expval(qml.PauliZ(0))

interface_tensors = [[0, 1], np.array([0, 1]), torch.Tensor([0, 1]), tf.Variable([0, 1], dtype=float), jnp.array([0, 1])]
for tensor in interface_tensors:
res = circuit(weight=tensor)
print(f"Result value: {res:.2f}; Result type: {type(res)}")

Result value: 1.00; Result type: <class 'pennylane.numpy.tensor.tensor'>
Result value: 1.00; Result type: <class 'pennylane.numpy.tensor.tensor'>
Result value: 1.00; Result type: <class 'torch.Tensor'>
Result value: 1.00; Result type: <class 'tensorflow.python.framework.ops.EagerTensor'>
Result value: 1.00; Result type: <class 'jaxlib.xla_extension.Array'>


• JAX-JIT support for computing the gradient of QNodes that return a single vector of probabilities or multiple expectation values is now available. (#3244) (#3261)

import jax
from jax import numpy as jnp
from jax.config import config
config.update("jax_enable_x64", True)

dev = qml.device("lightning.qubit", wires=2)

@jax.jit
@qml.qnode(dev, diff_method="parameter-shift", interface="jax")
def circuit(x, y):
qml.RY(x, wires=0)
qml.RY(y, wires=1)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))

x = jnp.array(1.0)
y = jnp.array(2.0)

>>> jax.jacobian(circuit, argnums=[0, 1])(x, y)
(Array([-0.84147098,  0.35017549], dtype=float64, weak_type=True),
Array([ 4.47445479e-18, -4.91295496e-01], dtype=float64, weak_type=True))


Note that this change depends on jax.pure_callback, which requires jax>=0.3.17.

#### Construct Pauli words and sentences 🔤

• We’ve reorganized and grouped everything in PennyLane responsible for manipulating Pauli operators into a pauli module. The grouping module has been deprecated as a result, and logic was moved from pennylane/grouping to pennylane/pauli/grouping. (#3179)

• qml.pauli.PauliWord and qml.pauli.PauliSentence can be used to represent tensor products and linear combinations of Pauli operators, respectively. These provide a more performant method to compute sums and products of Pauli operators. (#3195)

• qml.pauli.PauliWord represents tensor products of Pauli operators. We can efficiently multiply and extract the matrix of these operators using this representation.

>>> pw1 = qml.pauli.PauliWord({0:"X", 1:"Z"})
>>> pw2 = qml.pauli.PauliWord({0:"Y", 1:"Z"})
>>> pw1, pw2
(X(0) @ Z(1), Y(0) @ Z(1))
>>> pw1 * pw2
(Z(0), 1j)
>>> pw1.to_mat(wire_order=[0,1])
array([[ 0,  0,  1,  0],
[ 0,  0,  0, -1],
[ 1,  0,  0,  0],
[ 0, -1,  0,  0]])

• qml.pauli.PauliSentence represents linear combinations of Pauli words. We can efficiently add, multiply and extract the matrix of these operators in this representation.

>>> ps1 = qml.pauli.PauliSentence({pw1: 1.2, pw2: 0.5j})
>>> ps2 = qml.pauli.PauliSentence({pw1: -1.2})
>>> ps1
1.2 * X(0) @ Z(1)
+ 0.5j * Y(0) @ Z(1)
>>> ps1 + ps2
0.0 * X(0) @ Z(1)
+ 0.5j * Y(0) @ Z(1)
>>> ps1 * ps2
-1.44 * I
+ (-0.6+0j) * Z(0)
>>> (ps1 + ps2).to_mat(wire_order=[0,1])
array([[ 0. +0.j,  0. +0.j,  0.5+0.j,  0. +0.j],
[ 0. +0.j,  0. +0.j,  0. +0.j, -0.5+0.j],
[-0.5+0.j,  0. +0.j,  0. +0.j,  0. +0.j],
[ 0. +0.j,  0.5+0.j,  0. +0.j,  0. +0.j]])


#### (Experimental) More support for multi-measurement and gradient output types 🧪

• qml.enable_return() now supports QNodes returning multiple measurements, including shots vectors, and gradient output types. (#2886) (#3052) (#3041) (#3090) (#3069) (#3137) (#3127) (#3099) (#3098) (#3095) (#3091) (#3176) (#3170) (#3194) (#3267) (#3234) (#3232) (#3223) (#3222) (#3315)

In v0.25, we introduced qml.enable_return(), which separates measurements into their own tensors. The motivation of this change is the deprecation of ragged ndarray creation in NumPy.

With this release, we’re continuing to elevate this feature by adding support for:

• Execution (qml.execute)

• Jacobian vector product (JVP) computation

• Gradient transforms (qml.gradients.param_shift, qml.gradients.finite_diff, qml.gradients.hessian_transform, qml.gradients.param_shift_hessian).

• Interfaces (Autograd, TensorFlow, and JAX, although without JIT)

With this added support, the JAX interface can handle multiple shots (shots vectors), measurements, and gradient output types with qml.enable_return():

import jax

qml.enable_return()
dev = qml.device("default.qubit", wires=2, shots=(1, 10000))

params = jax.numpy.array([0.1, 0.2])

@qml.qnode(dev, interface="jax", diff_method="parameter-shift", max_diff=2)
def circuit(x):
qml.RX(x[0], wires=[0])
qml.RY(x[1], wires=[1])
qml.CNOT(wires=[0, 1])
return qml.var(qml.PauliZ(0) @ qml.PauliX(1)), qml.probs(wires=[0])

>>> jax.hessian(circuit)(params)
((Array([[ 0.,  0.],
[ 2., -3.]], dtype=float32),
Array([[[-0.5,  0. ],
[ 0. ,  0. ]],
[[ 0.5,  0. ],
[ 0. ,  0. ]]], dtype=float32)),
(Array([[ 0.07677898,  0.0563341 ],
[ 0.07238522, -1.830669  ]], dtype=float32),
Array([[[-4.9707499e-01,  2.9999996e-04],
[-6.2500127e-04,  1.2500001e-04]],
[[ 4.9707499e-01, -2.9999996e-04],
[ 6.2500127e-04, -1.2500001e-04]]], dtype=float32)))


For more details, please refer to the documentation.

#### New basis rotation and tapering features in qml.qchem 🤓

• Grouped coefficients, observables, and basis rotation transformation matrices needed to construct a qubit Hamiltonian in the rotated basis of molecular orbitals are now calculable via qml.qchem.basis_rotation(). (#3011)

>>> symbols  = ['H', 'H']
>>> geometry = np.array([[0.0, 0.0, 0.0], [1.398397361, 0.0, 0.0]], requires_grad = False)
>>> mol = qml.qchem.Molecule(symbols, geometry)
>>> core, one, two = qml.qchem.electron_integrals(mol)()
>>> coeffs, ops, unitaries = qml.qchem.basis_rotation(one, two, tol_factor=1.0e-5)
>>> unitaries
[tensor([[-1.00000000e+00, -5.46483514e-13],
tensor([[-1.00000000e+00,  3.17585063e-14],
tensor([[-0.70710678, -0.70710678],
tensor([[ 2.58789009e-11,  1.00000000e+00],

• Any gate operation can now be tapered according to $$\mathbb{Z}_2$$ symmetries of the Hamiltonian via qml.qchem.taper_operation. (#3002) (#3121)

>>> symbols = ['He', 'H']
>>> geometry =  np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.4589]])
>>> mol = qml.qchem.Molecule(symbols, geometry, charge=1)
>>> H, n_qubits = qml.qchem.molecular_hamiltonian(symbols, geometry)
>>> generators = qml.qchem.symmetry_generators(H)
>>> paulixops = qml.qchem.paulix_ops(generators, n_qubits)
>>> paulix_sector = qml.qchem.optimal_sector(H, generators, mol.n_electrons)
>>> tap_op = qml.qchem.taper_operation(qml.SingleExcitation, generators, paulixops,
...                paulix_sector, wire_order=H.wires, op_wires=[0, 2])
>>> tap_op(3.14159)
[Exp(1.5707949999999993j PauliY)]


Moreover, the obtained tapered operation can be used directly within a QNode.

>>> dev = qml.device('default.qubit', wires=[0, 1])
>>> @qml.qnode(dev)
... def circuit(params):
...     tap_op(params[0])
...     return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))
>>> drawer = qml.draw(circuit, show_all_wires=True)
>>> print(drawer(params=[3.14159]))
0: ──Exp(0.00+1.57j Y)─┤ ╭<[email protected]>
1: ────────────────────┤ ╰<[email protected]>

• Functionality has been added to estimate the number of measurements required to compute an expectation value with a target error and estimate the error in computing an expectation value with a given number of measurements. (#3000)

#### New functions, operations, and observables 🤩

• Wires of operators or entire QNodes can now be mapped to other wires via qml.map_wires(). (#3143) (#3145)

The qml.map_wires() function requires a dictionary representing a wire map. Use it with

• arbitrary operators:

>>> op = qml.RX(0.54, wires=0) + qml.PauliX(1) + (qml.PauliZ(2) @ qml.RY(1.23, wires=3))
>>> op
(RX(0.54, wires=[0]) + PauliX(wires=[1])) + (PauliZ(wires=[2]) @ RY(1.23, wires=[3]))
>>> wire_map = {0: 10, 1: 11, 2: 12, 3: 13}
>>> qml.map_wires(op, wire_map)
(RX(0.54, wires=[10]) + PauliX(wires=[11])) + (PauliZ(wires=[12]) @ RY(1.23, wires=[13]))


A map_wires method has also been added to operators, which returns a copy of the operator with its wires changed according to the given wire map.

• entire QNodes:

dev = qml.device("default.qubit", wires=["A", "B", "C", "D"])
wire_map = {0: "A", 1: "B", 2: "C", 3: "D"}

@qml.qnode(dev)
def circuit():
qml.RX(0.54, wires=0)
qml.PauliX(1)
qml.PauliZ(2)
qml.RY(1.23, wires=3)
return qml.probs(wires=0)

>>> mapped_circuit = qml.map_wires(circuit, wire_map)
>>> mapped_circuit()
>>> print(qml.draw(mapped_circuit)())
A: ──RX(0.54)─┤  Probs
B: ──X────────┤
C: ──Z────────┤
D: ──RY(1.23)─┤

• The qml.IntegerComparator arithmetic operation is now available. (#3113)

Given a basis state $$\vert n \rangle$$, where $$n$$ is a positive integer, and a fixed positive integer $$L$$, qml.IntegerComparator flips a target qubit if $$n \geq L$$. Alternatively, the flipping condition can be $$n < L$$ as demonstrated below:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit():
qml.BasisState(np.array([0, 1]), wires=range(2))
qml.IntegerComparator(2, geq=False, wires=[0, 1])
return qml.state()

>>> circuit()
[-0.5+0.j  0.5+0.j -0.5+0.j  0.5+0.j]

• The qml.GellMann qutrit observable, the ternary generalization of the Pauli observables, is now available. (#3035)

When using qml.GellMann, the index keyword argument determines which of the 8 Gell-Mann matrices is used.

dev = qml.device("default.qutrit", wires=2)

@qml.qnode(dev)
def circuit():
qml.TClock(wires=0)
qml.TShift(wires=1)
return qml.expval(qml.GellMann(wires=0, index=8) + qml.GellMann(wires=1, index=3))

>>> circuit()
-0.42264973081037416

• Controlled qutrit operations can now be performed with qml.ControlledQutritUnitary. (#2844)

The control wires and values that define the operation are defined analogously to the qubit operation.

dev = qml.device("default.qutrit", wires=3)

@qml.qnode(dev)
def circuit(U):
qml.TShift(wires=0)
qml.ControlledQutritUnitary(U, control_wires=[0, 1], control_values='12', wires=2)
return qml.state()

>>> U = np.array([[1, 1, 0], [1, -1, 0], [0, 0, np.sqrt(2)]]) / np.sqrt(2)
>>> circuit(U)
tensor([0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,
0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,
0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,


### Improvements

• PennyLane now supports Python 3.11! (#3297)

• qml.sample and qml.counts work more efficiently and track if computational basis samples are being generated when they are called without specifying an observable. (#3207)

• The parameters of a basis set containing a different number of Gaussian functions are now easier to differentiate. (#3213)

• Printing a qml.MultiControlledX operator now shows the control_values keyword argument. (#3113)

• qml.simplify and transforms like qml.matrix, batch_transform, hamiltonian_expand, and split_non_commuting now work with QuantumScript as well as QuantumTape. (#3209)

• A redundant flipping of the initial state in the UCCSD and kUpCCGSD templates has been removed. (#3148)

• qml.adjoint now supports batching if the base operation supports batching. (#3168)

• qml.OrbitalRotation is now decomposed into two qml.SingleExcitation operations for faster execution and more efficient parameter-shift gradient calculations on devices that natively support qml.SingleExcitation. (#3171)

• The Exp class decomposes into a PauliRot class if the coefficient is imaginary and the base operator is a Pauli Word. (#3249)

• Added the operator attributes has_decomposition and has_adjoint that indicate whether a corresponding decomposition or adjoint method is available. (#2986)

• Structural improvements are made to QueuingManager, formerly QueuingContext, and AnnotatedQueue. (#2794) (#3061) (#3085)

• QueuingContext is renamed to QueuingManager.

• QueuingManager should now be the global communication point for putting queuable objects into the active queue.

• QueuingManager is no longer an abstract base class.

• AnnotatedQueue and its children no longer inherit from QueuingManager.

• QueuingManager is no longer a context manager.

• Recording queues should start and stop recording via the QueuingManager.add_active_queue and QueuingContext.remove_active_queue class methods instead of directly manipulating the _active_contexts property.

• AnnotatedQueue and its children no longer provide global information about actively recording queues. This information is now only available through QueuingManager.

• AnnotatedQueue and its children no longer have the private _append, _remove, _update_info, _safe_update_info, and _get_info methods. The public analogues should be used instead.

• QueuingManager.safe_update_info and AnnotatedQueue.safe_update_info are deprecated. Their functionality is moved to update_info.

• qml.Identity now accepts multiple wires.

(#3049)

>>> id_op = qml.Identity([0, 1])
>>> id_op.matrix()
array([[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]])
>>> id_op.sparse_matrix()
<4x4 sparse matrix of type '<class 'numpy.float64'>'
with 4 stored elements in Compressed Sparse Row format>
>>> id_op.eigvals()
array([1., 1., 1., 1.])

• Added unitary_check keyword argument to the constructor of the QubitUnitary class which indicates whether the user wants to check for unitarity of the input matrix or not. Its default value is false. (#3063)

• Modified the representation of WireCut by using qml.draw_mpl. (#3067)

• Improved the performance of qml.math.expand_matrix function for dense and sparse matrices. (#3060) (#3064)

• Added support for sums and products of operator classes with scalar tensors of any interface (NumPy, JAX, Tensorflow, PyTorch…). (#3149)

>>> s_prod = torch.tensor(4) * qml.RX(1.23, 0)
>>> s_prod
4*(RX(1.23, wires=[0]))
>>> s_prod.scalar
tensor(4)

• Added overlapping_ops property to the Composite class to improve the performance of the eigvals, diagonalizing_gates and Prod.matrix methods. (#3084)

• Added the map_wires method to the operators, which returns a copy of the operator with its wires changed according to the given wire map. (#3143)

>>> op = qml.Toffoli([0, 1, 2])
>>> wire_map = {0: 2, 2: 0}
>>> op.map_wires(wire_map=wire_map)
Toffoli(wires=[2, 1, 0])

• Calling compute_matrix and compute_sparse_matrix of simple non-parametric operations is now faster and more memory-efficient with the addition of caching. (#3134)

• Added details to the output of Exp.label(). (#3126)

• qml.math.unwrap no longer creates ragged arrays. Lists remain lists. (#3163)

• New null.qubit device. The null.qubitperforms no operations or memory allocations. (#2589)

• default.qubit favours decomposition and avoids matrix construction for QFT and GroverOperator at larger qubit numbers. (#3193)

• qml.ControlledQubitUnitary now has a control_values property. (#3206)

• Added a new qml.tape.QuantumScript class that contains all the non-queuing behavior of QuantumTape. Now, QuantumTape inherits from QuantumScript as well as AnnotatedQueue. (#3097)

• Extended the qml.equal function to MeasurementProcesses (#3189)

• qml.drawer.draw.draw_mpl now accepts a style kwarg to select a style for plotting, rather than calling qml.drawer.use_style(style) before plotting. Setting a style for draw_mpl does not change the global configuration for matplotlib plotting. If no style is passed, the function defaults to plotting with the black_white style. (#3247)

### Breaking changes

• QuantumTape._par_info is now a list of dictionaries, instead of a dictionary whose keys are integers starting from zero. (#3185)

• QueuingContext has been renamed to QueuingManager. (#3061)

• Deprecation patches for the return types enum’s location and qml.utils.expand are removed. (#3092)

• _multi_dispatch functionality has been moved inside the get_interface function. This function can now be called with one or multiple tensors as arguments. (#3136)

>>> torch_scalar = torch.tensor(1)
>>> torch_tensor = torch.Tensor([2, 3, 4])
>>> numpy_tensor = np.array([5, 6, 7])
>>> qml.math.get_interface(torch_scalar)
'torch'
>>> qml.math.get_interface(numpy_tensor)
'numpy'


_multi_dispatch previously had only one argument which contained a list of the tensors to be dispatched:

>>> qml.math._multi_dispatch([torch_scalar, torch_tensor, numpy_tensor])
'torch'


To differentiate whether the user wants to get the interface of a single tensor or multiple tensors, get_interface now accepts a different argument per tensor to be dispatched:

>>> qml.math.get_interface(*[torch_scalar, torch_tensor, numpy_tensor])
'torch'
>>> qml.math.get_interface(torch_scalar, torch_tensor, numpy_tensor)
'torch'

• Operator.compute_terms is removed. On a specific instance of an operator, op.terms() can be used instead. There is no longer a static method for this. (#3215)

### Deprecations

• QueuingManager.safe_update_info and AnnotatedQueue.safe_update_info are deprecated. Instead, update_info no longer raises errors

if the object isn’t in the queue. (#3085)

• qml.tape.stop_recording and QuantumTape.stop_recording have been moved to qml.QueuingManager.stop_recording. The old functions will still be available until v0.29. (#3068)

• qml.tape.get_active_tape has been deprecated. Use qml.QueuingManager.active_context() instead. (#3068)

• Operator.compute_terms has been removed. On a specific instance of an operator, use op.terms() instead. There is no longer a static method for this. (#3215)

• qml.tape.QuantumTape.inv() has been deprecated. Use qml.tape.QuantumTape.adjoint instead. (#3237)

• qml.transforms.qcut.remap_tape_wires has been deprecated. Use qml.map_wires instead. (#3186)

• The grouping module qml.grouping has been deprecated. Use qml.pauli or qml.pauli.grouping instead. The module will still be available until v0.28. (#3262)

### Documentation

• The code block in the usage details of the UCCSD template has been updated. (#3140)

• Added a “Deprecations” page to the developer documentation. (#3093)

• The example of the qml.FlipSign template has been updated. (#3219)

### Bug fixes

• qml.SparseHamiltonian now validates the size of the input matrix. (#3278)

• Users no longer see unintuitive errors when inputing sequences to qml.Hermitian. (#3181)

• The evaluation of QNodes that return either vn_entropy or mutual_info raises an informative error message when using devices that define a vector of shots. (#3180)

• Fixed a bug that made qml.AmplitudeEmbedding incompatible with JITting. (#3166)

• Fixed the qml.transforms.transpile transform to work correctly for all two-qubit operations. (#3104)

• Fixed a bug with the control values of a controlled version of a ControlledQubitUnitary. (#3119)

• Fixed a bug where qml.math.fidelity(non_trainable_state, trainable_state) failed unexpectedly. (#3160)

• Fixed a bug where qml.QueuingManager.stop_recording did not clean up if yielded code raises an exception. (#3182)

• Returning qml.sample() or qml.counts() with other measurements of non-commuting observables now raises a QuantumFunctionError (e.g., return qml.expval(PauliX(wires=0)), qml.sample() now raises an error). (#2924)

• Fixed a bug where op.eigvals() would return an incorrect result if the operator was a non-hermitian composite operator. (#3204)

• Fixed a bug where qml.BasisStatePreparation and qml.BasisEmbedding were not jit-compilable with JAX. (#3239)

• Fixed a bug where qml.MottonenStatePreparation was not jit-compilable with JAX. (#3260)

• Fixed a bug where qml.MottonenStatePreparation was not jit-compilable with JAX. (#3260)

• Fixed a bug where qml.expval(qml.Hamiltonian()) would not raise an error if the Hamiltonian involved some wires that are not present on the device. (#3266)

• Fixed a bug where qml.tape.QuantumTape.shape() did not account for the batch dimension of the tape (#3269)

### Contributors

This release contains contributions from (in alphabetical order):

Kamal Mohamed Ali, Guillermo Alonso-Linaje, Juan Miguel Arrazola, Utkarsh Azad, Thomas Bromley, Albert Mitjans Coma, Isaac De Vlugt, Olivia Di Matteo, Amintor Dusko, Lillian M. A. Frederiksen, Diego Guala, Josh Izaac, Soran Jahangiri, Edward Jiang, Korbinian Kottmann, Christina Lee, Romain Moyard, Lee J. O’Riordan, Mudit Pandey, Matthew Silverman, Jay Soni, Antal Száva, David Wierichs,

orphan

## Release 0.26.0¶

### New features since last release

• PennyLane now provides built-in support for implementing the classical-shadows measurement protocol. (#2820) (#2821) (#2871) (#2968) (#2959) (#2968)

The classical-shadow measurement protocol is described in detail in the paper Predicting Many Properties of a Quantum System from Very Few Measurements. As part of the support for classical shadows in this release, two new finite-shot and fully-differentiable measurements are available:

• QNodes returning the new measurement qml.classical_shadow() will return two entities; bits (0 or 1 if the 1 or -1 eigenvalue is sampled, respectively) and recipes (the randomized Pauli measurements that are performed for each qubit, labelled by integer):

dev = qml.device("default.qubit", wires=2, shots=3)

@qml.qnode(dev)
def circuit():
qml.CNOT(wires=[0, 1])

>>> bits, recipes = circuit()
>>> bits
tensor([[0, 0],
[1, 0],
>>> recipes
tensor([[2, 2],
[0, 2],

• QNodes returning qml.shadow_expval() yield the expectation value estimation using classical shadows:

dev = qml.device("default.qubit", wires=range(2), shots=10000)

@qml.qnode(dev)
def circuit(x, H):
qml.CNOT((0,1))
qml.RX(x, wires=0)

H = qml.Hamiltonian(
[1., 1.],
[qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1)]
)

>>> circuit(x, H)
-0.4797000000000001


Fully-differentiable QNode transforms for both new classical-shadows measurements are also available via qml.shadows.shadow_state and qml.shadows.shadow_expval, respectively.

For convenient post-processing, we’ve also added the ability to calculate general Renyi entropies by way of the ClassicalShadow class’ entropy method, which requires the wires of the subsystem of interest and the Renyi entropy order:

>>> shadow = qml.ClassicalShadow(bits, recipes)
>>> vN_entropy = shadow.entropy(wires=[0, 1], alpha=1)


#### Qutrits: quantum circuits for tertiary degrees of freedom ☘️

• An entirely new framework for quantum computing is now simulatable with the addition of qutrit functionalities. (#2699) (#2781) (#2782) (#2783) (#2784) (#2841) (#2843)

Qutrits are like qubits, but instead live in a three-dimensional Hilbert space; they are not binary degrees of freedom, they are tertiary. The advent of qutrits allows for all sorts of interesting theoretical, practical, and algorithmic capabilities that have yet to be discovered.

To facilitate qutrit circuits requires a new device: default.qutrit. The default.qutrit device is a Python-based simulator, akin to default.qubit, and is defined as per usual:

>>> dev = qml.device("default.qutrit", wires=1)


The following operations are supported on default.qutrit devices:

• The qutrit shift operator, qml.TShift, and the ternary clock operator, qml.TClock, as defined in this paper by Yeh et al. (2022), which are the qutrit analogs of the Pauli X and Pauli Z operations, respectively.

• The qml.TAdd and qml.TSWAP operations which are the qutrit analogs of the CNOT and SWAP operations, respectively.

• Custom unitary operations via qml.QutritUnitary.

• qml.state and qml.probs measurements.

• Measuring user-specified Hermitian matrix observables via qml.THermitian.

A comprehensive example of these features is given below:

dev = qml.device("default.qutrit", wires=1)

U = np.array([
[1, 1, 1],
[1, 1, 1],
[1, 1, 1]
]
) / np.sqrt(3)

obs = np.array([
[1, 1, 0],
[1, -1, 0],
[0, 0, np.sqrt(2)]
]
) / np.sqrt(2)

@qml.qnode(dev)
def qutrit_state(U, obs):
qml.TShift(0)
qml.TClock(0)
qml.QutritUnitary(U, wires=0)
return qml.state()

@qml.qnode(dev)
def qutrit_expval(U, obs):
qml.TShift(0)
qml.TClock(0)
qml.QutritUnitary(U, wires=0)
return qml.expval(qml.THermitian(obs, wires=0))

>>> qutrit_state(U, obs)
>>> qutrit_expval(U, obs)


We will continue to add more and more support for qutrits in future releases.

#### Simplifying just got... simpler 😌

• The qml.simplify() function has several intuitive improvements with this release. (#2978) (#2982) (#2922) (#3012)

qml.simplify can now perform the following:

• simplify parametrized operations

• simplify the adjoint and power of specific operators

• group like terms in a sum

• resolve products of Pauli operators

• combine rotation angles of identical rotation gates

Here is an example of qml.simplify in action with parameterized rotation gates. In this case, the angles of rotation are simplified to be modulo $$4\pi$$.

>>> op1 = qml.RX(30.0, wires=0)
>>> qml.simplify(op1)
RX(4.867258771281655, wires=[0])
>>> op2 = qml.RX(4 * np.pi, wires=0)
>>> qml.simplify(op2)
Identity(wires=[0])


All of these simplification features can be applied directly to quantum functions, QNodes, and tapes via decorating with @qml.simplify, as well:

dev = qml.device("default.qubit", wires=2)
@qml.simplify
@qml.qnode(dev)
def circuit():
qml.adjoint(qml.prod(qml.RX(1, 0) ** 1, qml.RY(1, 0), qml.RZ(1, 0)))
return qml.probs(wires=0)

>>> circuit()
>>> list(circuit.tape)
[RZ(11.566370614359172, wires=[0]) @ RY(11.566370614359172, wires=[0]) @ RX(11.566370614359172, wires=[0]),
probs(wires=[0])]


#### QNSPSA optimizer 💪

• A new optimizer called qml.QNSPSAOptimizer is available that implements the quantum natural simultaneous perturbation stochastic approximation (QNSPSA) method based on Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information. (#2818)

qml.QNSPSAOptimizer is a second-order SPSA algorithm, which combines the convergence power of the quantum-aware Quantum Natural Gradient (QNG) optimization method with the reduced quantum evaluations of SPSA methods.

While the QNSPSA optimizer requires additional circuit executions (10 executions per step) compared to standard SPSA optimization (3 executions per step), these additional evaluations are used to provide a stochastic estimation of a second-order metric tensor, which often helps the optimizer to achieve faster convergence.

Use qml.QNSPSAOptimizer like you would any other optimizer:

max_iterations = 50
opt = qml.QNSPSAOptimizer()

for _ in range(max_iterations):
params, cost = opt.step_and_cost(cost, params)


#### Operator and parameter broadcasting supplements 📈

• Operator methods for exponentiation and raising to a power have been added. (#2799) (#3029)

• The qml.exp function can be used to create observables or generic rotation gates:

>>> x = 1.234
>>> t = qml.PauliX(0) @ qml.PauliX(1) + qml.PauliY(0) @ qml.PauliY(1)
>>> isingxy = qml.exp(t, 0.25j * x)
>>> isingxy.matrix()
array([[1.       +0.j        , 0.       +0.j        ,
1.       +0.j        , 0.       +0.j        ],
[0.       +0.j        , 0.8156179+0.j        ,
1.       +0.57859091j, 0.       +0.j        ],
[0.       +0.j        , 0.       +0.57859091j,
0.8156179+0.j        , 0.       +0.j        ],
[0.       +0.j        , 0.       +0.j        ,
1.       +0.j        , 1.       +0.j        ]])

• The qml.pow function raises a given operator to a power:

>>> op = qml.pow(qml.PauliX(0), 2)
>>> op.matrix()
array([[1, 0], [0, 1]])

• An operator called qml.PSWAP is now available. (#2667)

The qml.PSWAP gate – or phase-SWAP gate – was previously available within the PennyLane-Braket plugin only. Enjoy it natively in PennyLane with v0.26.

• Check whether or not an operator is hermitian or unitary with qml.is_hermitian and qml.is_unitary. (#2960)

>>> op1 = qml.PauliX(wires=0)
>>> qml.is_hermitian(op1)
True
>>> op2 = qml.PauliX(0) + qml.RX(np.pi/3, 0)
>>> qml.is_unitary(op2)
False

• Embedding templates now support parameter broadcasting. (#2810)

Embedding templates like AmplitudeEmbedding or IQPEmbedding now support parameter broadcasting with a leading broadcasting dimension in their variational parameters. AmplitudeEmbedding, for example, would usually use a one-dimensional input vector of features. With broadcasting, we can now compute

>>> features = np.array([
...     [0.5, 0.5, 0., 0., 0.5, 0., 0.5, 0.],
...     [1., 0., 0., 0., 0., 0., 0., 0.],
...     [0.5, 0.5, 0., 0., 0., 0., 0.5, 0.5],
... ])
>>> op = qml.AmplitudeEmbedding(features, wires=[1, 5, 2])
>>> op.batch_size
3


An exception is BasisEmbedding, which is not broadcastable.

### Improvements

• The qml.math.expand_matrix() method now allows the sparse matrix representation of an operator to be extended to a larger hilbert space. (#2998)

>>> from scipy import sparse
>>> mat = sparse.csr_matrix([[0, 1], [1, 0]])
>>> qml.math.expand_matrix(mat, wires=[1], wire_order=[0,1]).toarray()
array([[0., 1., 0., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 1.],
[0., 0., 1., 0.]])

• qml.ctrl now uses Controlled instead of ControlledOperation. The new Controlled class wraps individual Operator‘s instead of a tape. It provides improved representations and integration. (#2990)

• qml.matrix can now compute the matrix of tapes and QNodes that contain multiple broadcasted operations or non-broadcasted operations after broadcasted ones. (#3025)

A common scenario in which this becomes relevant is the decomposition of broadcasted operations: the decomposition in general will contain one or multiple broadcasted operations as well as operations with no or fixed parameters that are not broadcasted.

• Lists of operators are now internally sorted by their respective wires while also taking into account their commutativity property. (#2995)

• Some methods of the QuantumTape class have been simplified and reordered to improve both readability and performance. (#2963)

• The qml.qchem.molecular_hamiltonian function is modified to support observable grouping. (#2997)

• qml.ops.op_math.Controlled now has basic decomposition functionality. (#2938)

• Automatic circuit cutting has been improved by making better partition imbalance derivations. Now it is more likely to generate optimal cuts for larger circuits. (#2517)

• By default, qml.counts only returns the outcomes observed in sampling. Optionally, specifying qml.counts(all_outcomes=True) will return a dictionary containing all possible outcomes. (#2889)

>>> dev = qml.device("default.qubit", wires=2, shots=1000)
>>>
>>> @qml.qnode(dev)
>>> def circuit():
...     qml.CNOT(wires=[0, 1])
...     return qml.counts(all_outcomes=True)
>>> result = circuit()
>>> result
{'00': 495, '01': 0, '10': 0,  '11': 505}

• Internal use of in-place inversion is eliminated in preparation for its deprecation. (#2965)

• Controlled operators now work with qml.is_commuting. (#2994)

• qml.prod and qml.op_sum now support the sparse_matrix() method. (#3006)

>>> xy = qml.prod(qml.PauliX(1), qml.PauliY(1))
>>> op = qml.op_sum(xy, qml.Identity(0))
>>>
>>> sparse_mat = op.sparse_matrix(wire_order=[0,1])
>>> type(sparse_mat)
<class 'scipy.sparse.csr.csr_matrix'>
>>> sparse_mat.toarray()
[[1.+1.j 0.+0.j 0.+0.j 0.+0.j]
[0.+0.j 1.-1.j 0.+0.j 0.+0.j]
[0.+0.j 0.+0.j 1.+1.j 0.+0.j]
[0.+0.j 0.+0.j 0.+0.j 1.-1.j]]

• Provided sparse_matrix() support for single qubit observables. (#2964)

• qml.Barrier with only_visual=True now simplifies via op.simplify() to the identity operator or a product of identity operators. (#3016)

• More accurate and intuitive outputs for printing some operators have been added. (#3013)

• Results for the matrix of the sum or product of operators are stored in a more efficient manner. (#3022)

• The computation of the (sparse) matrix for the sum or product of operators is now more efficient. (#3030)

• When the factors of qml.prod don’t share any wires, the matrix and sparse matrix are computed using a kronecker product for improved efficiency. (#3040)

• qml.grouping.is_pauli_word now returns False for operators that don’t inherit from qml.Observable instead of raising an error. (#3039)

• Added functionality to iterate over operators created from qml.op_sum and qml.prod. (#3028)

>>> op = qml.op_sum(qml.PauliX(0), qml.PauliY(1), qml.PauliZ(2))
>>> len(op)
3
>>> op[1]
PauliY(wires=[1])
>>> [o.name for o in op]
['PauliX', 'PauliY', 'PauliZ']


### Deprecations

• In-place inversion is now deprecated. This includes op.inv() and op.inverse=value. Please use qml.adjoint or qml.pow instead. Support for these methods will remain till v0.28. (#2988)

Don’t use:

>>> v1 = qml.PauliX(0).inv()
>>> v2 = qml.PauliX(0)
>>> v2.inverse = True


>>> qml.adjoint(qml.PauliX(0))
>>> qml.pow(qml.PauliX(0), -1)
PauliX(wires=[0])**-1
>>> qml.pow(qml.PauliX(0), -1, lazy=False)
PauliX(wires=[0])
>>> qml.PauliX(0) ** -1
PauliX(wires=[0])**-1


qml.adjoint takes the conjugate transpose of an operator, while qml.pow(op, -1) indicates matrix inversion. For unitary operators, adjoint will be more efficient than qml.pow(op, -1), even though they represent the same thing.

• The supports_reversible_diff device capability is unused and has been removed. (#2993)

### Breaking changes

• Measuring an operator that might not be hermitian now raises a warning instead of an error. To definitively determine whether or not an operator is hermitian, use qml.is_hermitian. (#2960)

• The ControlledOperation class has been removed. This was a developer-only class, so the change should not be evident to any users. It is replaced by Controlled. (#2990)

• The default execute method for the QubitDevice base class now calls self.statistics with an additional keyword argument circuit, which represents the quantum tape being executed. Any device that overrides statistics should edit the signature of the method to include the new circuit keyword argument. (#2820)

• The expand_matrix() has been moved from pennylane.operation to pennylane.math.matrix_manipulation (#3008)

• qml.grouping.utils.is_commuting has been removed, and its Pauli word logic is now part of qml.is_commuting. (#3033)

• qml.is_commuting has been moved from pennylane.transforms.commutation_dag to pennylane.ops.functions. (#2991)

### Documentation

• Updated the Fourier transform docs to use circuit_spectrum instead of spectrum, which has been deprecated. (#3018)

• Corrected the docstrings for diagonalizing gates for all relevant operations. The docstrings used to say that the diagonalizing gates implemented $$U$$, the unitary such that $$O = U \Sigma U^{\dagger}$$, where $$O$$ is the original observable and $$\Sigma$$ a diagonal matrix. However, the diagonalizing gates actually implement $$U^{\dagger}$$, since $$\langle \psi | O | \psi \rangle = \langle \psi | U \Sigma U^{\dagger} | \psi \rangle$$, making $$U^{\dagger} | \psi \rangle$$ the actual state being measured in the Z-basis. (#2981)

### Bug fixes

• Fixed a bug with qml.ops.Exp operators when the coefficient is autograd but the diagonalizing gates don’t act on all wires. (#3057)

• Fixed a bug where the tape transform single_qubit_fusion computed wrong rotation angles for specific combinations of rotations. (#3024)

• Jax gradients now work with a QNode when the quantum function was transformed by qml.simplify. (#3017)

• Operators that have num_wires = AnyWires or num_wires = AnyWires now raise an error, with certain exceptions, when instantiated with wires=[]. (#2979)

• Fixed a bug where printing qml.Hamiltonian with complex coefficients raises TypeError in some cases. (#3004)

• Added a more descriptive error message when measuring non-commuting observables at the end of a circuit with probs, samples, counts and allcounts. (#3065)

### Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Utkarsh Azad, Tom Bromley, Olivia Di Matteo, Isaac De Vlugt, Yiheng Duan, Lillian Marie Austin Frederiksen, Josh Izaac, Soran Jahangiri, Edward Jiang, Ankit Khandelwal, Korbinian Kottmann, Meenu Kumari, Christina Lee, Albert Mitjans Coma, Romain Moyard, Rashid N H M, Zeyue Niu, Mudit Pandey, Matthew Silverman, Jay Soni, Antal Száva, Cody Wang, David Wierichs.

orphan

## Release 0.25.1¶

### Bug fixes

• Fixed Torch device discrepencies for certain parametrized operations by updating qml.math.array and qml.math.eye to preserve the Torch device used. (#2967)

### Contributors

This release contains contributions from (in alphabetical order):

Romain Moyard, Rashid N H M, Lee James O’Riordan, Antal Száva

orphan

## Release 0.25.0¶

### New features since last release

#### Estimate computational resource requirements 🧠

• Functionality for estimating molecular simulation computations has been added with qml.resource. (#2646) (#2653) (#2665) (#2694) (#2720) (#2723) (#2746) (#2796) (#2797) (#2874) (#2944) (#2644)

The new resource module allows you to estimate the number of non-Clifford gates and logical qubits needed to implement quantum phase estimation algorithms for simulating materials and molecules. This includes support for quantum algorithms using first and second quantization with specific bases:

• First quantization using a plane-wave basis via the FirstQuantization class:

>>> n = 100000        # number of plane waves
>>> eta = 156         # number of electrons
>>> omega = 1145.166  # unit cell volume in atomic units
>>> algo = FirstQuantization(n, eta, omega)
>>> print(algo.gates, algo.qubits)
1.10e+13, 4416

• Second quantization with a double-factorized Hamiltonian via the DoubleFactorization class:

symbols = ["O", "H", "H"]
geometry = np.array(
[
[0.00000000, 0.00000000, 0.28377432],
[0.00000000, 1.45278171, -1.00662237],
[0.00000000, -1.45278171, -1.00662237],
],
)

mol = qml.qchem.Molecule(symbols, geometry, basis_name="sto-3g")
core, one, two = qml.qchem.electron_integrals(mol)()

algo = DoubleFactorization(one, two)

>>> print(algo.gates, algo.qubits)
103969925, 290


The methods of the FirstQuantization and the DoubleFactorization classes, such as qubit_cost (number of logical qubits) and gate_cost (number of non-Clifford gates), can be also accessed as static methods:

>>> qml.resource.FirstQuantization.qubit_cost(100000, 156, 169.69608, 0.01)
4377
>>> qml.resource.FirstQuantization.gate_cost(100000, 156, 169.69608, 0.01)
3676557345574


#### Differentiable error mitigation ⚙️

• Differentiable zero-noise-extrapolation (ZNE) error mitigation is now available. (#2757)

Elevate any variational quantum algorithm to a mitigated algorithm with improved results on noisy hardware while maintaining differentiability throughout.

In order to do so, use the qml.transforms.mitigate_with_zne transform on your QNode and provide the PennyLane proprietary qml.transforms.fold_global folding function and qml.transforms.poly_extrapolate extrapolation function. Here is an example for a noisy simulation device where we mitigate a QNode and are still able to compute the gradient:

# Describe noise
noise_gate = qml.DepolarizingChannel
noise_strength = 0.1

dev_ideal = qml.device("default.mixed", wires=1)
dev_noisy = qml.transforms.insert(noise_gate, noise_strength)(dev_ideal)

scale_factors = [1, 2, 3]
@mitigate_with_zne(
scale_factors,
qml.transforms.fold_global,
qml.transforms.poly_extrapolate,
extrapolate_kwargs={'order': 2}
)
@qml.qnode(dev_noisy)
def qnode_mitigated(theta):
qml.RY(theta, wires=0)
return qml.expval(qml.PauliX(0))

>>> theta = np.array(0.5, requires_grad=True)
0.5712737447327619


#### More native support for parameter broadcasting 📡

• default.qubit now natively supports parameter broadcasting, providing increased performance when executing the same circuit at various parameter positions compared to manually looping over parameters, or directly using the qml.transforms.broadcast_expand transform. (#2627)

dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev)
def circuit(x):
qml.RX(x, wires=0)
return qml.expval(qml.PauliZ(0))

>>> circuit(np.array([0.1, 0.3, 0.2]))


Currently, not all templates have been updated to support broadcasting.

• Parameter-shift gradients now allow for parameter broadcasting internally, which can result in a significant speedup when computing gradients of circuits with many parameters. (#2749)

The gradient transform qml.gradients.param_shift now accepts the keyword argument broadcast. If set to True, broadcasting is used to compute the derivative:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(x, y):
qml.RX(x, wires=0)
qml.RY(y, wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

>>> x = np.array([np.pi/3, np.pi/2], requires_grad=True)
>>> y = np.array([np.pi/6, np.pi/5], requires_grad=True)
(tensor([[-0.7795085,  0.       ],
tensor([[-0.125, 0.  ],


The following example highlights how to make use of broadcasting gradients at the QNode level. Internally, broadcasting is used to compute the parameter-shift rule when required, which may result in performance improvements.

@qml.qnode(dev, diff_method="parameter-shift", broadcast=True)
def circuit(x, y):
qml.RX(x, wires=0)
qml.RY(y, wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

>>> x = np.array(0.1, requires_grad=True)
(array(-0.09195267), array(-0.38747287))


Here, only 2 circuits are created internally, rather than 4 with broadcast=False.

To illustrate the speedup, for a constant-depth circuit with Pauli rotations and controlled Pauli rotations, the time required to compute qml.gradients.param_shift(circuit, broadcast=False)(params) (“No broadcasting”) and qml.gradients.param_shift(circuit, broadcast=True)(params) (“Broadcasting”) as a function of the number of qubits is given here.

• Operations for quantum chemistry now support parameter broadcasting. (#2726)

>>> op = qml.SingleExcitation(np.array([0.3, 1.2, -0.7]), wires=[0, 1])
>>> op.matrix().shape
(3, 4, 4)


#### Intuitive operator arithmetic 🧮

• New functionality for representing the sum, product, and scalar-product of operators is available. (#2475) (#2625) (#2622) (#2721)

The following functionalities have been added to facilitate creating new operators whose matrix, terms, and eigenvalues can be accessed as per usual, while maintaining differentiability. Operators created from these new features can be used within QNodes as operations or as observables (where physically applicable).

• Summing any number of operators via qml.op_sum results in a “summed” operator:

>>> ops_to_sum = [qml.PauliX(0), qml.PauliY(1), qml.PauliZ(0)]
>>> summed_ops = qml.op_sum(*ops_to_sum)
>>> summed_ops
PauliX(wires=[0]) + PauliY(wires=[1]) + PauliZ(wires=[0])
>>> qml.matrix(summed_ops)
array([[ 1.+0.j,  0.-1.j,  1.+0.j,  0.+0.j],
[ 0.+1.j,  1.+0.j,  0.+0.j,  1.+0.j],
[ 1.+0.j,  0.+0.j, -1.+0.j,  0.-1.j],
[ 0.+0.j,  1.+0.j,  0.+1.j, -1.+0.j]])
>>> summed_ops.terms()
([1.0, 1.0, 1.0], (PauliX(wires=[0]), PauliY(wires=[1]), PauliZ(wires=[0])))

• Multiplying any number of operators via qml.prod results in a “product” operator, where the matrix product or tensor product is used correspondingly:

>>> theta = 1.23
>>> prod_op = qml.prod(qml.PauliZ(0), qml.RX(theta, 1))
>>> prod_op
PauliZ(wires=[0]) @ RX(1.23, wires=[1])
>>> qml.eigvals(prod_op)
[-1.39373197 -0.23981492  0.23981492  1.39373197]

• Taking the product of a coefficient and an operator via qml.s_prod produces a “scalar-product” operator:

>>> sprod_op = qml.s_prod(2.0, qml.PauliX(0))
>>> sprod_op
2.0*(PauliX(wires=[0]))
>>> sprod_op.matrix()
array([[ 0., 2.],
[ 2., 0.]])
>>> sprod_op.terms()
([2.0], [PauliX(wires=[0])])


Each of these new functionalities can be used within QNodes as operators or observables, where applicable, while also maintaining differentiability. For example:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(angles):
qml.prod(qml.PauliZ(0), qml.RY(angles[0], 1))
qml.op_sum(qml.PauliX(1), qml.RY(angles[1], 0))

return qml.expval(qml.op_sum(qml.PauliX(0), qml.PauliZ(1)))

>>> angles = np.array([1.23, 4.56], requires_grad=True)
>>> circuit(angles)
array([-0.9424888,  0.       ])

• All PennyLane operators can now be added, subtracted, multiplied, scaled, and raised to powers using +, -, @, *, **, respectively. (#2849) (#2825) (#2891)

• You can now add scalars to operators, where the interpretation is that the scalar is a properly-sized identity matrix;

>>> sum_op = 5 + qml.PauliX(0)
>>> sum_op.matrix()
array([[5., 1.],
[1., 5.]])

• The + and - operators can be used to combine all Pennylane operators:

>>> sum_op = qml.RX(phi=1.23, wires=0) + qml.RZ(phi=3.14, wires=0) - qml.RY(phi=0.12, wires=0)
>>> sum_op
RX(1.23, wires=[0]) + RZ(3.14, wires=[0]) + -1*(RY(0.12, wires=[0]))
>>> qml.matrix(sum_op)
array([[-0.18063077-0.99999968j,  0.05996401-0.57695852j],
[-0.05996401-0.57695852j, -0.18063077+0.99999968j]])


Note that the behavior of + and - with observables is different; it still creates a Hamiltonian.

• The * and @ operators can be used to scale and compose all PennyLane operators.

>>> prod_op = 2*qml.RX(1, wires=0) @ qml.RY(2, wires=0)
>>> prod_op
2*(RX(1, wires=[0])) @ RY(2, wires=[0])
>>> qml.matrix(prod_op)
array([[ 0.94831976-0.80684536j, -1.47692053-0.51806945j],
[ 1.47692053-0.51806945j,  0.94831976+0.80684536j]])

• The ** operator can be used to raise PennyLane operators to a power.

>>> exp_op = qml.RZ(1.0, wires=0) ** 2
>>> exp_op
RZ**2(1.0, wires=[0])
>>> qml.matrix(exp_op)
array([[0.54030231-0.84147098j, 0.        +0.j        ],
[0.        +0.j        , 0.54030231+0.84147098j]])

• A new class called Controlled is available in qml.ops.op_math to represent a controlled version of any operator. This will eventually be integrated into qml.ctrl to provide a performance increase and more feature coverage. (#2634)

• Arithmetic operations can now be simplified using qml.simplify. (#2835) (#2854)

>>> op = qml.adjoint(qml.adjoint(qml.RX(x, wires=0)))
>>> op
>>> qml.simplify(op)

• A new function called qml.equal can be used to compare the equality of parametric operators. (#2651)

>>> qml.equal(qml.RX(1.23, 0), qml.RX(1.23, 0))
True
>>> qml.equal(qml.RY(4.56, 0), qml.RY(7.89, 0))
False


#### Marvelous mixed state features 🙌

• The default.mixed device now supports backpropagation with the "jax" interface, which can result in significant speedups. (#2754) (#2776)

dev = qml.device("default.mixed", wires=2)

@qml.qnode(dev, diff_method="backprop", interface="jax")
def circuit(angles):
qml.RX(angles[0], wires=0)
qml.RY(angles[1], wires=1)
return qml.expval(qml.PauliZ(0) + qml.PauliZ(1))

>>> angles = np.array([np.pi/6, np.pi/5], requires_grad=True)
array([-0.8660254 , -0.25881905])


Additionally, quantum channels now support Jax and TensorFlow tensors. This allows quantum channels to be used inside QNodes decorated by tf.function, jax.jit, or jax.vmap.

• The default.mixed device now supports readout error. (#2786)

A new keyword argument called readout_prob can be specified when creating a default.mixed device. Any circuits running on a default.mixed device with a finite readout_prob (upper-bounded by 1) will alter the measurements performed at the end of the circuit similarly to how a qml.BitFlip channel would affect circuit measurements:

>>> dev = qml.device("default.mixed", wires=2, readout_prob=0.1)
>>> @qml.qnode(dev)
... def circuit():
...     return qml.expval(qml.PauliZ(0))
>>> circuit()
array(0.8)


#### Relative entropy is now available in qml.qinfo 💥

• The quantum information module now supports computation of relative entropy. (#2772)

We’ve enabled two cases for calculating the relative entropy:

• A QNode transform via qml.qinfo.relative_entropy:

dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(param):
qml.RY(param, wires=0)
qml.CNOT(wires=[0, 1])
return qml.state()

>>> relative_entropy_circuit = qml.qinfo.relative_entropy(circuit, circuit, wires0=[0], wires1=[0])
>>> x, y = np.array(0.4), np.array(0.6)
>>> relative_entropy_circuit((x,), (y,))
0.017750012490703237

• Support in qml.math for flexible post-processing:

>>> rho = np.array([[0.3, 0], [0, 0.7]])
>>> sigma = np.array([[0.5, 0], [0, 0.5]])
>>> qml.math.relative_entropy(rho, sigma)


#### New measurements, operators, and more! ✨

• A new measurement called qml.counts is available. (#2686) (#2839) (#2876)

QNodes with shots != None that return qml.counts will yield a dictionary whose keys are bitstrings representing computational basis states that were measured, and whose values are the corresponding counts (i.e., how many times that computational basis state was measured):

dev = qml.device("default.qubit", wires=2, shots=1000)

@qml.qnode(dev)
def circuit():
qml.CNOT(wires=[0, 1])
return qml.counts()

>>> circuit()
{'00': 495, '11': 505}


qml.counts can also accept observables, where the resulting dictionary is ordered by the eigenvalues of the observable.

dev = qml.device("default.qubit", wires=2, shots=1000)

@qml.qnode(dev)
def circuit():
qml.CNOT(wires=[0, 1])
return qml.counts(qml.PauliZ(0)), qml.counts(qml.PauliZ(1))

>>> circuit()
({-1: 470, 1: 530}, {-1: 470, 1: 530})

• A new experimental return type for QNodes with multiple measurements has been added. (#2814) (#2815) (#2860)

QNodes returning a list or tuple of different measurements return an intuitive data structure via qml.enable_return(), where the individual measurements are separated into their own tensors:

qml.enable_return()
dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(x):
qml.CRX(x, wires=[0, 1])
return (qml.probs(wires=[0]), qml.vn_entropy(wires=[0]), qml.probs(wires=0), qml.expval(wires=1))

>>> circuit(0.5)


In addition, QNodes that utilize this new return type support backpropagation. This new return type can be disabled thereafter via qml.disable_return().

• An operator called qml.FlipSign is now available. (#2780)

Mathematically, qml.FlipSign functions as follows: $$\text{FlipSign}(n) \vert m \rangle = (-1)^\delta_{n,m} \vert m \rangle$$, where $$\vert m \rangle$$ is an arbitrary qubit state and $n$ is a qubit configuration:

basis_state = [0, 1]

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit():
for wire in list(range(2)):
qml.FlipSign(basis_state, wires = list(range(2)))
return qml.state()

>>> circuit()
tensor([ 0.5+0.j  -0.5+0.j 0.5+0.j  0.5+0.j], requires_grad=True)

• The simultaneous perturbation stochastic approximation (SPSA) optimizer is available via qml.SPSAOptimizer. (#2661)

The SPSA optimizer is suitable for cost functions whose evaluation may involve noise. Use the SPSA optimizer like you would any other optimizer:

max_iterations = 50
opt = qml.SPSAOptimizer(maxiter=max_iterations)

for _ in range(max_iterations):
params, cost = opt.step_and_cost(cost, params)


#### More drawing styles 🎨

• New PennyLane-inspired sketch and sketch_dark styles are now available for drawing circuit diagram graphics. (#2709)

### Improvements 📈

• default.qubit now natively executes any operation that defines a matrix except for trainable Pow operations. (#2836)

• Added expm to the qml.math module for matrix exponentiation. (#2890)

• When adjoint differentiation is requested, circuits are now decomposed so that all trainable operations have a generator. (#2836)

• A warning is now emitted for qml.state, qml.density_matrix, qml.vn_entropy, and qml.mutual_info when using a device with finite shots or a shot list since these measurements are always analytic. (#2918)

• The efficiency of the Hartree-Fock workflow has been improved by removing repetitive steps. (#2850)

• The coefficients of the non-differentiable molecular Hamiltonians generated with openfermion now have requires_grad = False by default. (#2865)

• Upgraded performance of the compute_matrix method of broadcastable parametric operations. (#2759)

• Jacobians are now cached with the Autograd interface when using the parameter-shift rule. (#2645)

• The qml.state and qml.density_matrix measurements now support custom wire labels. (#2779)

• Add trivial behaviour logic to qml.operation.expand_matrix. (#2785)

• Added an are_pauli_words_qwc function which checks if certain Pauli words are pairwise qubit-wise commuting. This new function improves performance when measuring hamiltonians with many commuting terms. (#2789)

### Breaking changes 💔

• The deprecated qml.hf module is removed. Users with code that calls qml.hf can simply replace qml.hf with qml.qchem in most cases, or refer to the qchem documentation and demos for more information. (#2795)

• default.qubit now uses stopping_condition to specify support for anything with a matrix. To override this behavior in inheriting devices and to support only a specific subset of operations, developers need to override stopping_condition. (#2836)

• Custom devices inheriting from DefaultQubit or QubitDevice can break due to the introduction of parameter broadcasting. (#2627)

A custom device should only break if all three following statements hold simultaneously:

1. The custom device inherits from DefaultQubit, not QubitDevice.

2. The device implements custom methods in the simulation pipeline that are incompatible with broadcasting (for example expval, apply_operation or analytic_probability).

3. The custom device maintains the flag "supports_broadcasting": True in its capabilities dictionary or it overwrites Device.batch_transform without applying broadcast_expand (or both).

The capabilities["supports_broadcasting"] is set to True for DefaultQubit. Typically, the easiest fix will be to change the capabilities["supports_broadcasting"] flag to False for the child device and/or to include a call to broadcast_expand in CustomDevice.batch_transform, similar to how Device.batch_transform calls it.

Separately from the above, custom devices that inherit from QubitDevice and implement a custom _gather method need to allow for the kwarg axis to be passed to this _gather method.

• The argument argnum of the function qml.batch_input has been redefined: now it indicates the indices of the batched parameters, which need to be non-trainable, in the quantum tape. Consequently, its default value (set to 0) has been removed. (#2873)

Before this breaking change, one could call qml.batch_input without any arguments when using batched inputs as the first argument of the quantum circuit.

dev = qml.device("default.qubit", wires=2, shots=None)

@qml.batch_input()  # argnum = 0
@qml.qnode(dev, diff_method="parameter-shift", interface="tf")
def circuit(inputs, weights):  # argument inputs is batched
qml.RY(weights[0], wires=0)
qml.AngleEmbedding(inputs, wires=range(2), rotation="Y")
qml.RY(weights[1], wires=1)
return qml.expval(qml.PauliZ(1))


With this breaking change, users must set a value to argnum specifying the index of the batched inputs with respect to all quantum tape parameters. In this example the quantum tape parameters are [ weights[0], inputs, weights[1] ], thus argnum should be set to 1, specifying that inputs is batched:

dev = qml.device("default.qubit", wires=2, shots=None)

@qml.batch_input(argnum=1)
@qml.qnode(dev, diff_method="parameter-shift", interface="tf")
def circuit(inputs, weights):
qml.RY(weights[0], wires=0)
qml.AngleEmbedding(inputs, wires=range(2), rotation="Y")
qml.RY(weights[1], wires=1)
return qml.expval(qml.PauliZ(1))

• PennyLane now depends on newer versions (>=2.7) of the semantic_version package, which provides an updated API that is incompatible which versions of the package prior to 2.7. If you run into issues relating to this package, please reinstall PennyLane. (#2744) (#2767)

### Documentation 📕

• Added a dedicated docstring for the QubitDevice.sample method. (#2812)

• Optimization examples of using JAXopt and Optax with the JAX interface have been added. (#2769)

• Updated IsingXY gate docstring. (#2858)

### Bug fixes 🐞

• Fixes qml.equal so that operators with different inverse properties are not equal. (#2947)

• Cleans up interactions between operator arithmetic and batching by testing supported cases and adding errors when batching is not supported. (#2900)

• Fixed a bug where the parameter-shift rule wasn’t defined for qml.kUpCCGSD. (#2913)

• Reworked the Hermiticity check in qml.Hermitian by using qml.math calls because calling .conj() on an EagerTensor from TensorFlow raised an error. (#2895)

• Fixed a bug where the parameter-shift gradient breaks when using both custom grad_recipes that contain unshifted terms and recipes that do not contain any unshifted terms. (#2834)

• Fixed mixed CPU-GPU data-locality issues for the Torch interface. (#2830)

• Fixed a bug where the parameter-shift Hessian of circuits with untrainable parameters might be computed with respect to the wrong parameters or might raise an error. (#2822)

• Fixed a bug where the custom implementation of the states_to_binary device method was not used. (#2809)

• qml.grouping.group_observables now works when individual wire labels are iterable. (#2752)

• The adjoint of an adjoint now has a correct expand result. (#2766)

• Fixed the ability to return custom objects as the expectation value of a QNode with the Autograd interface. (#2808)

• The WireCut operator now raises an error when instantiating it with an empty list. (#2826)

• Hamiltonians with grouped observables are now allowed to be measured on devices which were transformed using qml.transform.insert(). (#2857)

• Fixed a bug where qml.batch_input raised an error when using a batched operator that was not located at the beginning of the circuit. In addition, now qml.batch_input raises an error when using trainable batched inputs, which avoids an unwanted behaviour with duplicated parameters. (#2873)

• Calling qml.equal with nested operators now raises a NotImplementedError. (#2877)

• Fixed a bug where a non-sensible error message was raised when using qml.counts with shots=False. (#2928)

• Fixed a bug where no error was raised and a wrong value was returned when using qml.counts with another non-commuting observable. (#2928)

• Operator Arithmetic now allows Hamiltonian objects to be used and produces correct matrices. (#2957)

### Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Utkarsh Azad, Samuel Banning, Prajwal Borkar, Isaac De Vlugt, Olivia Di Matteo, Kristiyan Dilov, David Ittah, Josh Izaac, Soran Jahangiri, Edward Jiang, Ankit Khandelwal, Korbinian Kottmann, Meenu Kumari, Christina Lee, Sergio Martínez-Losa, Albert Mitjans Coma, Ixchel Meza Chavez, Romain Moyard, Lee James O’Riordan, Mudit Pandey, Bogdan Reznychenko, Shuli Shu, Jay Soni, Modjtaba Shokrian-Zini, Antal Száva, David Wierichs, Moritz Willmann

orphan

## Release 0.24.0¶

### New features since last release

#### All new quantum information quantities 📏

• Functionality for computing quantum information quantities for QNodes has been added. (#2554) (#2569) (#2598) (#2617) (#2631) (#2640) (#2663) (#2684) (#2688) (#2695) (#2710) (#2712)

This includes two new QNode measurements:

• The Von Neumann entropy via qml.vn_entropy:

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit_entropy(x):
...     qml.IsingXX(x, wires=[0,1])
...     return qml.vn_entropy(wires=[0], log_base=2)
>>> circuit_entropy(np.pi/2)
1.0

• The mutual information via qml.mutual_info:

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit(x):
...     qml.IsingXX(x, wires=[0,1])
...     return qml.mutual_info(wires0=[0], wires1=[1], log_base=2)
>>> circuit(np.pi/2)
2.0


New differentiable transforms are also available in the qml.qinfo module:

• The classical and quantum Fisher information via qml.qinfo.classical_fisher, qml.qinfo.quantum_fisher, respectively:

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev)
def circ(params):
qml.RY(params[0], wires=1)
qml.CNOT(wires=(1,0))
qml.RY(params[1], wires=1)
qml.RZ(params[2], wires=1)
return qml.expval(qml.PauliX(0) @ qml.PauliX(1) - 0.5 * qml.PauliZ(1))

params = np.array([0.5, 1., 0.2], requires_grad=True)
cfim = qml.qinfo.classical_fisher(circ)(params)
qfim = qml.qinfo.quantum_fisher(circ)(params)


These quantities are typically employed in variational optimization schemes to tilt the gradient in a more favourable direction — producing what is known as the natural gradient. For example:

>>> grad = qml.grad(circ)(params)
[ 5.94225615e-01 -2.61509542e-02 -1.18674655e-18]
[ 0.59422561 -0.02615095 -0.03989212]

• The fidelity between two arbitrary states via qml.qinfo.fidelity:

dev = qml.device('default.qubit', wires=1)

@qml.qnode(dev)
def circuit_rx(x):
qml.RX(x[0], wires=0)
qml.RZ(x[1], wires=0)
return qml.state()

@qml.qnode(dev)
def circuit_ry(y):
qml.RY(y, wires=0)
return qml.state()

>>> x = np.array([0.1, 0.3], requires_grad=True)
>>> fid_func = qml.qinfo.fidelity(circuit_rx, circuit_ry, wires0=[0], wires1=[0])
>>> fid_func(x, y)
0.9905158135644924
>>> df(x, y)
(array([-0.04768725, -0.29183666]), array(-0.09489803))

• Reduced density matrices of arbitrary states via qml.qinfo.reduced_dm:

dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(x):
qml.IsingXX(x, wires=[0,1])
return qml.state()

>>> qml.qinfo.reduced_dm(circuit, wires=[0])(np.pi/2)
[[0.5+0.j 0.+0.j]
[0.+0.j 0.5+0.j]]

• Similar transforms, qml.qinfo.vn_entropy and qml.qinfo.mutual_info exist for transforming QNodes.

Currently, all quantum information measurements and transforms are differentiable, but only support statevector devices, with hardware support to come in a future release (with the exception of qml.qinfo.classical_fisher and qml.qinfo.quantum_fisher, which are both hardware compatible).

For more information, check out the new qinfo module and measurements page.

• In addition to the QNode transforms and measurements above, functions for computing and differentiating quantum information metrics with numerical statevectors and density matrices have been added to the qml.math module. This enables flexible custom post-processing.

• qml.math.reduced_dm

• qml.math.vn_entropy

• qml.math.mutual_info

• qml.math.fidelity

For example:

>>> x = torch.tensor([1.0, 0.0, 0.0, 1.0], requires_grad=True)
>>> en = qml.math.vn_entropy(x / np.sqrt(2.), indices=[0])
>>> en
>>> en.backward()
tensor([-0.3069,  0.0000,  0.0000, -0.3069])


#### Faster mixed-state training with backpropagation 📉

• The default.mixed device now supports differentiation via backpropagation with the Autograd, TensorFlow, and PyTorch (CPU) interfaces, leading to significantly more performant optimization and training. (#2615) (#2670) (#2680)

As a result, the default differentiation method for the device is now "backprop". To continue using the old default "parameter-shift", explicitly specify this differentiation method in the QNode:

dev = qml.device("default.mixed", wires=2)

def circuit(x):
qml.RY(x, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(wires=1))

>>> x = np.array(0.5, requires_grad=True)
>>> circuit(x)
array(0.87758256)
-0.479425538604203


#### Support for quantum parameter broadcasting 📡

• Quantum operators, functions, and tapes now support broadcasting across parameter dimensions, making it more convenient for developers to execute their PennyLane programs with multiple sets of parameters. (#2575) (#2609)

Parameter broadcasting refers to passing tensor parameters with additional leading dimensions to quantum operators; additional dimensions will flow through the computation, and produce additional dimensions at the output.

For example, instantiating a rotation gate with a one-dimensional array leads to a broadcasted Operation:

>>> x = np.array([0.1, 0.2, 0.3], requires_grad=True)
>>> op = qml.RX(x, 0)
>>> op.batch_size
3


Its matrix correspondingly is augmented by a leading dimension of size batch_size:

>>> np.round(qml.matrix(op), 4)
tensor([[[0.9988+0.j    , 0.    -0.05j  ],
[0.    -0.05j  , 0.9988+0.j    ]],
[[0.995 +0.j    , 0.    -0.0998j],
[0.    -0.0998j, 0.995 +0.j    ]],
[[0.9888+0.j    , 0.    -0.1494j],
>>> qml.matrix(op).shape
(3, 2, 2)


This can be extended to quantum functions, where we may mix-and-match operations with batched parameters and those without. However, the batch_size of each batched Operator within the quantum function must be the same:

>>> dev = qml.device('default.qubit', wires=1)
>>> @qml.qnode(dev)
... def circuit_rx(x, z):
...     qml.RX(x, wires=0)
...     qml.RZ(z, wires=0)
...     qml.RY(0.3, wires=0)
...     return qml.probs(wires=0)
>>> circuit_rx([0.1, 0.2], [0.3, 0.4])
tensor([[0.97092256, 0.02907744],


Parameter broadcasting is supported on all devices, hardware and simulator. Note that if not natively supported by the underlying device, parameter broadcasting may result in additional quantum device evaluations.

• A new transform, qml.transforms.broadcast_expand, has been added, which automates the process of transforming quantum functions (and tapes) to multiple quantum evaluations with no parameter broadcasting. (#2590)

>>> dev = qml.device('default.qubit', wires=1)
>>> @qml.qnode(dev)
... def circuit_rx(x, z):
...     qml.RX(x, wires=0)
...     qml.RZ(z, wires=0)
...     qml.RY(0.3, wires=0)
...     return qml.probs(wires=0)
>>> print(qml.draw(circuit_rx)([0.1, 0.2], [0.3, 0.4]))
0: ──RX(0.10)──RZ(0.30)──RY(0.30)─┤  Probs
\
0: ──RX(0.20)──RZ(0.40)──RY(0.30)─┤  Probs


Under-the-hood, this transform is used for devices that don’t natively support parameter broadcasting.

• To specify that a device natively supports broadcasted tapes, the new flag Device.capabilities()["supports_broadcasting"] should be set to True.

• To support parameter broadcasting for new or custom operations, the following new Operator class attributes must be specified:

• Operator.ndim_params specifies expected number of dimensions for each parameter

Once set, Operator.batch_size and QuantumTape.batch_size will dynamically compute the parameter broadcasting axis dimension, if present.

#### Improved JAX JIT support 🏎

• JAX just-in-time (JIT) compilation now supports vector-valued QNodes, enabling new types of workflows and significant performance boosts. (#2034)

Vector-valued QNodes include those with:

• qml.probs;

• qml.state;

• qml.sample or

• multiple qml.expval / qml.var measurements.

Consider a QNode that returns basis-state probabilities:

dev = qml.device('default.qubit', wires=2)
x = jnp.array(0.543)
y = jnp.array(-0.654)

@jax.jit
@qml.qnode(dev, diff_method="parameter-shift", interface="jax")
def circuit(x, y):
qml.RX(x, wires=[0])
qml.RY(y, wires=[1])
qml.CNOT(wires=[0, 1])
return qml.probs(wires=[1])

>>> circuit(x, y)
Array([0.8397495 , 0.16025047], dtype=float32)


Note that computing the jacobian of vector-valued QNode is not supported with JAX JIT. The output of vector-valued QNodes can, however, be used in the definition of scalar-valued cost functions whose gradients can be computed.

For example, one can define a cost function that outputs the first element of the probability vector:

def cost(x, y):
return circuit(x, y)[0]

>>> jax.grad(cost, argnums=[0])(x, y)
(Array(-0.2050439, dtype=float32),)


#### More drawing styles 🎨

• New solarized_light and solarized_dark styles are available for drawing circuit diagram graphics. (#2662)

#### New operations & transforms 🤖

• The qml.IsingXY gate is now available (see 1912.04424). (#2649)

• The qml.ECR (echoed cross-resonance) operation is now available (see 2105.01063). This gate is a maximally-entangling gate and is equivalent to a CNOT gate up to single-qubit pre-rotations. (#2613)

• The adjoint transform adjoint can now accept either a single instantiated operator or a quantum function. It returns an entity of the same type / call signature as what it was given: (#2222) (#2672)

>>> qml.adjoint(qml.PauliX(0))


Now, adjoint wraps operators in a symbolic operator class qml.ops.op_math.Adjoint. This class should not be constructed directly; the adjoint constructor should always be used instead. The class behaves just like any other Operator:

>>> op = qml.adjoint(qml.S(0))
>>> qml.matrix(op)
array([[1.-0.j, 0.-0.j],
[0.-0.j, 0.-1.j]])
>>> qml.eigvals(op)
array([1.-0.j, 0.-1.j])

• A new symbolic operator class qml.ops.op_math.Pow represents an operator raised to a power. When decomposition() is called, a list of new operators equal to this one raised to the given power is given: (#2621)

>>> op = qml.ops.op_math.Pow(qml.PauliX(0), 0.5)
>>> op.decomposition()
[SX(wires=[0])]
>>> qml.matrix(op)
array([[0.5+0.5j, 0.5-0.5j],
[0.5-0.5j, 0.5+0.5j]])

• A new transform qml.batch_partial is available which behaves similarly to functools.partial, but supports batching in the unevaluated parameters. (#2585)

This is useful for executing a circuit with a batch dimension in some of its parameters:

dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev)
def circuit(x, y):
qml.RX(x, wires=0)
qml.RY(y, wires=0)
return qml.expval(qml.PauliZ(wires=0))

>>> batched_partial_circuit = qml.batch_partial(circuit, x=np.array(np.pi / 4))
>>> y = np.array([0.2, 0.3, 0.4])
>>> batched_partial_circuit(y=y)

• A new transform qml.split_non_commuting is available, which splits a quantum function or tape into multiple functions/tapes determined by groups of commuting observables: (#2587)

dev = qml.device("default.qubit", wires=1)

@qml.transforms.split_non_commuting
@qml.qnode(dev)
def circuit(x):
qml.RX(x,wires=0)
return [qml.expval(qml.PauliX(0)), qml.expval(qml.PauliZ(0))]

>>> print(qml.draw(circuit)(0.5))
0: ──RX(0.50)─┤  <X>
\
0: ──RX(0.50)─┤  <Z>


### Improvements

• Expectation values of multiple non-commuting observables from within a single QNode are now supported: (#2587)

>>> dev = qml.device('default.qubit', wires=1)
>>> @qml.qnode(dev)
... def circuit_rx(x, z):
...     qml.RX(x, wires=0)
...     qml.RZ(z, wires=0)
...     return qml.expval(qml.PauliX(0)), qml.expval(qml.PauliY(0))
>>> circuit_rx(0.1, 0.3)

• Selecting which parts of parameter-shift Hessians are computed is now possible. (#2538)

The argnum keyword argument for qml.gradients.param_shift_hessian is now allowed to be a two-dimensional Boolean array_like. Only the indicated entries of the Hessian will then be computed.

A particularly useful example is the computation of the diagonal of the Hessian:

dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev)
def circuit(x):
qml.RX(x[0], wires=0)
qml.RY(x[1], wires=0)
qml.RX(x[2], wires=0)
return qml.expval(qml.PauliZ(0))

argnum = qml.math.eye(3, dtype=bool)
x = np.array([0.2, -0.9, 1.1], requires_grad=True)

>>> qml.gradients.param_shift_hessian(circuit, argnum=argnum)(x)
tensor([[-0.09928388,  0.        ,  0.        ],
[ 0.        , -0.27633945,  0.        ],
[ 0.        ,  0.        , -0.09928388]], requires_grad=True)

• Commuting Pauli operators are now measured faster. (#2425)

The logic that checks for qubit-wise commuting (QWC) observables has been improved, resulting in a performance boost that is noticable when many commuting Pauli operators of the same type are measured.

• It is now possible to add Observable objects to the integer 0, for example qml.PauliX(wires=[0]) + 0. (#2603)

• Wires can now be passed as the final argument to an Operator, instead of requiring the wires to be explicitly specified with keyword wires. This functionality already existed for Observables, but now extends to all Operators: (#2432)

>>> qml.S(0)
S(wires=[0])
>>> qml.CNOT((0,1))
CNOT(wires=[0, 1])

• The qml.taper function can now be used to consistently taper any additional observables such as dipole moment, particle number, and spin operators using the symmetries obtained from the Hamiltonian. (#2510)

• Sparse Hamiltonians’ representation has changed from Coordinate (COO) to Compressed Sparse Row (CSR) format. (#2561)

The CSR representation is more performant for arithmetic operations and matrix-vector products. This change decreases the expval() calculation time for qml.SparseHamiltonian, specially for large workflows. In addition, the CSR format consumes less memory for qml.SparseHamiltonian storage.

• IPython now displays the str representation of a Hamiltonian, rather than the repr. This displays more information about the object. (#2648)

• The qml.qchem tests have been restructured. (#2593) (#2545)

• OpenFermion-dependent tests are now localized and collected in tests.qchem.of_tests. The new module test_structure is created to collect the tests of the qchem.structure module in one place and remove their dependency to OpenFermion.

• Test classes have been created to group the integrals and matrices unit tests.

• An operations_only argument is introduced to the tape.get_parameters method. (#2543)

• The gradients module now uses faster subroutines and uniform formats of gradient rules. (#2452)

• Instead of checking types, objects are now processed in the QuantumTape based on a new _queue_category property. This is a temporary fix that will disappear in the future. (#2408)

• The QNode class now contains a new method best_method_str that returns the best differentiation method for a provided device and interface, in human-readable format. (#2533)

• Using Operation.inv() in a queuing environment no longer updates the queue’s metadata, but merely updates the operation in place. (#2596)

• A new method safe_update_info is added to qml.QueuingContext. This method is substituted for qml.QueuingContext.update_info in a variety of places. (#2612) (#2675)

• BasisEmbedding can accept an int as argument instead of a list of bits. (#2601)

For example, qml.BasisEmbedding(4, wires = range(4)) is now equivalent to qml.BasisEmbedding([0,1,0,0], wires = range(4)) (as 4==0b100).

• Introduced a new is_hermitian property to Operators to determine if an operator can be used in a measurement process. (#2629)

• Added separate requirements_dev.txt for separation of concerns for code development and just using PennyLane. (#2635)

• The performance of building sparse Hamiltonians has been improved by accumulating the sparse representation of coefficient-operator pairs in a temporary storage and by eliminating unnecessary kron operations on identity matrices. (#2630)

• Control values are now displayed distinctly in text and matplotlib drawings of circuits. (#2668)

• The TorchLayer init_method argument now accepts either a torch.nn.init function or a dictionary which should specify a torch.nn.init/torch.Tensor for each different weight. (#2678)

• The unused keyword argument do_queue for Operation.adjoint is now fully removed. (#2583)

• Several non-decomposable Adjoint operators are added to the device test suite. (#2658)

• The developer-facing pow method has been added to Operator with concrete implementations for many classes. (#2225)

• The ctrl transform and ControlledOperation have been moved to the new qml.ops.op_math submodule. The developer-facing ControlledOperation class is no longer imported top-level. (#2656)

### Deprecations

• qml.ExpvalCost has been deprecated, and usage will now raise a warning. (#2571)

Instead, it is recommended to simply pass Hamiltonians to the qml.expval function inside QNodes:

@qml.qnode(dev)
def ansatz(params):
some_qfunc(params)
return qml.expval(Hamiltonian)


### Breaking changes

• When using qml.TorchLayer, weights with negative shapes will now raise an error, while weights with size = 0 will result in creating empty Tensor objects. (#2678)

• PennyLane no longer supports TensorFlow <=2.3. (#2683)

• The qml.queuing.Queue class has been removed. (#2599)

• The qml.utils.expand function is now removed; qml.operation.expand_matrix should be used instead. (#2654)

• The module qml.gradients.param_shift_hessian has been renamed to qml.gradients.parameter_shift_hessian in order to distinguish it from the identically named function. Note that the param_shift_hessian function is unaffected by this change and can be invoked in the same manner as before via the qml.gradients module. (#2528)

• The properties eigval and matrix from the Operator class were replaced with the methods eigval() and matrix(wire_order=None). (#2498)

• Operator.decomposition() is now an instance method, and no longer accepts parameters. (#2498)

• Adds tests, adds no-coverage directives, and removes inaccessible logic to improve code coverage. (#2537)

• The base classes QubitDevice and DefaultQubit now accept data-types for a statevector. This enables a derived class (device) in a plugin to choose correct data-types: (#2448)

>>> dev = qml.device("default.qubit", wires=4, r_dtype=np.float32, c_dtype=np.complex64)
>>> dev.R_DTYPE
<class 'numpy.float32'>
>>> dev.C_DTYPE
<class 'numpy.complex64'>


### Bug fixes

• Fixed a bug where returning qml.density_matrix using the PyTorch interface would return a density matrix with wrong shape. (#2643)

• Fixed a bug to make param_shift_hessian work with QNodes in which gates marked as trainable do not have any impact on the QNode output. (#2584)

• QNodes can now interpret variations on the interface name, like "tensorflow" or "jax-jit", when requesting backpropagation. (#2591)

• Fixed a bug for diff_method="adjoint" where incorrect gradients were computed for QNodes with parametrized observables (e.g., qml.Hermitian). (#2543)

• Fixed a bug where QNGOptimizer did not work with operators whose generator was a Hamiltonian. (#2524)

• Fixed a bug with the decomposition of qml.CommutingEvolution. (#2542)

• Fixed a bug enabling PennyLane to work with the latest version of Autoray. (#2549)

• Fixed a bug which caused different behaviour for Hamiltonian @ Observable and Observable @ Hamiltonian. (#2570)

• Fixed a bug in DiagonalQubitUnitary._controlled where an invalid operation was queued instead of the controlled version of the diagonal unitary. (#2525)

• Updated the gradients fix to only apply to the strawberryfields.gbs device, since the original logic was breaking some devices. (#2485) (#2595)

• Fixed a bug in qml.transforms.insert where operations were not inserted after gates within a template. (#2704)

• Hamiltonian.wires is now properly updated after in place operations. (#2738)

### Documentation

• The centralized Xanadu Sphinx Theme is now used to style the Sphinx documentation. (#2450)

• Added a reference to qml.utils.sparse_hamiltonian in qml.SparseHamiltonian to clarify how to construct sparse Hamiltonians in PennyLane. (2572)

• Added a new section in the Gradients and Training page that summarizes the supported device configurations and provides justification. In addition, code examples were added for some selected configurations. (#2540)

• Added a note for the Depolarization Channel that specifies how the channel behaves for the different values of depolarization probability p. (#2669)

• The quickstart documentation has been improved. (#2530) (#2534) (#2564 (#2565 (#2566) (#2607) (#2608)

• The quantum chemistry quickstart documentation has been improved. (#2500)

• Testing documentation has been improved. (#2536)

• Documentation for the pre-commit package has been added. (#2567)

• Documentation for draw control wires change has been updated. (#2682)

### Contributors

This release contains contributions from (in alphabetical order):

Guillermo Alonso-Linaje, Mikhail Andrenkov, Juan Miguel Arrazola, Ali Asadi, Utkarsh Azad, Samuel Banning, Avani Bhardwaj, Thomas Bromley, Albert Mitjans Coma, Isaac De Vlugt, Amintor Dusko, Trent Fridey, Christian Gogolin, Qi Hu, Katharine Hyatt, David Ittah, Josh Izaac, Soran Jahangiri, Edward Jiang, Nathan Killoran, Korbinian Kottmann, Ankit Khandelwal, Christina Lee, Chae-Yeun Park, Mason Moreland, Romain Moyard, Maria Schuld, Jay Soni, Antal Száva, tal66, David Wierichs, Roeland Wiersema, WingCode.

orphan

## Release 0.23.1¶

### Bug fixes

• Fixed a bug enabling PennyLane to work with the latest version of Autoray. (#2548)

### Contributors

This release contains contributions from (in alphabetical order):

Josh Izaac

orphan

## Release 0.23.0¶

### New features since last release

#### More powerful circuit cutting ✂️

• Quantum circuit cutting (running N-wire circuits on devices with fewer than N wires) is now supported for QNodes of finite-shots using the new @qml.cut_circuit_mc transform. (#2313) (#2321) (#2332) (#2358) (#2382) (#2399) (#2407) (#2444)

With these new additions, samples from the original circuit can be simulated using a Monte Carlo method, using fewer qubits at the expense of more device executions. Additionally, this transform can take an optional classical processing function as an argument and return an expectation value.

The following 3-qubit circuit contains a WireCut operation and a sample measurement. When decorated with @qml.cut_circuit_mc, we can cut the circuit into two 2-qubit fragments:

dev = qml.device("default.qubit", wires=2, shots=1000)

@qml.cut_circuit_mc
@qml.qnode(dev)
def circuit(x):
qml.RX(0.89, wires=0)
qml.RY(0.5, wires=1)
qml.RX(1.3, wires=2)

qml.CNOT(wires=[0, 1])
qml.WireCut(wires=1)
qml.CNOT(wires=[1, 2])

qml.RX(x, wires=0)
qml.RY(0.7, wires=1)
qml.RX(2.3, wires=2)
return qml.sample(wires=[0, 2])


we can then execute the circuit as usual by calling the QNode:

>>> x = 0.3
>>> circuit(x)
tensor([[1, 1],
[0, 1],
[0, 1],
...,
[0, 1],
[0, 1],


Furthermore, the number of shots can be temporarily altered when calling the QNode:

>>> results = circuit(x, shots=123)
>>> results.shape
(123, 2)


The cut_circuit_mc transform also supports returning sample-based expectation values of observables using the classical_processing_fn argument. Refer to the UsageDetails section of the transform documentation for an example.

• The cut_circuit transform now supports automatic graph partitioning by specifying auto_cutter=True to cut arbitrary tape-converted graphs using the general purpose graph partitioning framework KaHyPar. (#2330) (#2428)

Note that KaHyPar needs to be installed separately with the auto_cutter=True option.

For integration with the existing low-level manual cut pipeline, refer to the documentation of the function .

@qml.cut_circuit(auto_cutter=True)
@qml.qnode(dev)
def circuit(x):
qml.RX(x, wires=0)
qml.RY(0.9, wires=1)
qml.RX(0.3, wires=2)
qml.CZ(wires=[0, 1])
qml.RY(-0.4, wires=0)
qml.CZ(wires=[1, 2])
return qml.expval(qml.grouping.string_to_pauli_word("ZZZ"))

>>> x = np.array(0.531, requires_grad=True)
>>> circuit(x)
0.47165198882111165
-0.276982865449393


#### Grand QChem unification ⚛️ 🏰

• Quantum chemistry functionality — previously split between an external pennylane-qchem package and internal qml.hf differentiable Hartree-Fock solver — is now unified into a single, included, qml.qchem module. (#2164) (#2385) (#2352) (#2420) (#2454)
(#2199) (#2371) (#2272) (#2230) (#2415) (#2426) (#2465)

The qml.qchem module provides a differentiable Hartree-Fock solver and the functionality to construct a fully-differentiable molecular Hamiltonian.

For example, one can continue to generate molecular Hamiltonians using
qml.qchem.molecular_hamiltonian:

symbols = ["H", "H"]
geometry = np.array([[0., 0., -0.66140414], [0., 0., 0.66140414]])
hamiltonian, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry, method="dhf")


By default, this will use the differentiable Hartree-Fock solver; however, simply set method="pyscf" to continue to use PySCF for Hartree-Fock calculations.

• Functions are added for building a differentiable dipole moment observable. Functions for computing multipole moment molecular integrals, needed for building the dipole moment observable, are also added. (#2173) (#2166)

The dipole moment observable can be constructed using qml.qchem.dipole_moment:

symbols  = ['H', 'H']
geometry = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]])
mol = qml.qchem.Molecule(symbols, geometry)
args = [geometry]
D = qml.qchem.dipole_moment(mol)(*args)

• The efficiency of computing molecular integrals and Hamiltonian is improved. This has been done by adding optimized functions for building fermionic and qubit observables and optimizing the functions used for computing the electron repulsion integrals. (#2316)

• The 6-31G basis set is added to the qchem basis set repo. This addition allows performing differentiable Hartree-Fock calculations with basis sets beyond the minimal sto-3g basis set for atoms with atomic number 1-10. (#2372)

The 6-31G basis set can be used to construct a Hamiltonian as

symbols = ["H", "H"]
geometry = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]])
H, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry, basis="6-31g")

• External dependencies are replaced with local functions for spin and particle number observables. (#2197) (#2362)

#### Pattern matching optimization 🔎 💎

• Added an optimization transform that matches pieces of user-provided identity templates in a circuit and replaces them with an equivalent component. (#2032)

For example, consider the following circuit where we want to replace sequence of two pennylane.S gates with a pennylane.PauliZ gate.

def circuit():
qml.S(wires=0)
qml.PauliZ(wires=0)
qml.S(wires=1)
qml.CZ(wires=[0, 1])
qml.S(wires=1)
qml.S(wires=2)
qml.CZ(wires=[1, 2])
qml.S(wires=2)
return qml.expval(qml.PauliX(wires=0))


We specify use the following pattern that implements the identity:

with qml.tape.QuantumTape() as pattern:
qml.S(wires=0)
qml.S(wires=0)
qml.PauliZ(wires=0)


To optimize the circuit with this identity pattern, we apply the qml.transforms.pattern_matching transform.

>>> dev = qml.device('default.qubit', wires=5)
>>> qnode = qml.QNode(circuit, dev)
>>> optimized_qfunc = qml.transforms.pattern_matching_optimization(pattern_tapes=[pattern])(circuit)
>>> optimized_qnode = qml.QNode(optimized_qfunc, dev)
>>> print(qml.draw(qnode)())
0: ──S──Z─╭C──────────┤  <X>
1: ──S────╰Z──S─╭C────┤
2: ──S──────────╰Z──S─┤
>>> print(qml.draw(optimized_qnode)())
0: ──S⁻¹─╭C────┤  <X>
1: ──Z───╰Z─╭C─┤
2: ──Z──────╰Z─┤


For more details on using pattern matching optimization you can check the corresponding documentation and also the following paper.

#### Measure the distance between two unitaries📏

• Added the HilbertSchmidt and the LocalHilbertSchmidt templates to be used for computing distance measures between unitaries. (#2364)

Given a unitary U, qml.HilberSchmidt can be used to measure the distance between unitaries and to define a cost function (cost_hst) used for learning a unitary V that is equivalent to U up to a global phase:

# Represents unitary U
with qml.tape.QuantumTape(do_queue=False) as u_tape:

# Represents unitary V
def v_function(params):
qml.RZ(params[0], wires=1)

@qml.qnode(dev)
def hilbert_test(v_params, v_function, v_wires, u_tape):
qml.HilbertSchmidt(v_params, v_function=v_function, v_wires=v_wires, u_tape=u_tape)
return qml.probs(u_tape.wires + v_wires)

def cost_hst(parameters, v_function, v_wires, u_tape):
return (1 - hilbert_test(v_params=parameters, v_function=v_function, v_wires=v_wires, u_tape=u_tape)[0])

>>> cost_hst(parameters=[0.1], v_function=v_function, v_wires=[1], u_tape=u_tape)


#### More tensor network support 🕸️

• Adds the qml.MERA template for implementing quantum circuits with the shape of a multi-scale entanglement renormalization ansatz (MERA). (#2418)

MERA follows the style of previous tensor network templates and is similar to quantum convolutional neural networks.

def block(weights, wires):
qml.CNOT(wires=[wires[0],wires[1]])
qml.RY(weights[0], wires=wires[0])
qml.RY(weights[1], wires=wires[1])

n_wires = 4
n_block_wires = 2
n_params_block = 2
n_blocks = qml.MERA.get_n_blocks(range(n_wires),n_block_wires)
template_weights = [[0.1,-0.3]]*n_blocks

dev= qml.device('default.qubit',wires=range(n_wires))
@qml.qnode(dev)
def circuit(template_weights):
qml.MERA(range(n_wires),n_block_wires,block, n_params_block, template_weights)
return qml.expval(qml.PauliZ(wires=1))


It may be necessary to reorder the wires to see the MERA architecture clearly:

>>> print(qml.draw(circuit,expansion_strategy='device',wire_order=[2,0,1,3])(template_weights))
2: ───────────────╭C──RY(0.10)──╭X──RY(-0.30)───────────────┤
0: ─╭X──RY(-0.30)─│─────────────╰C──RY(0.10)──╭C──RY(0.10)──┤
1: ─╰C──RY(0.10)──│─────────────╭X──RY(-0.30)─╰X──RY(-0.30)─┤  <Z>
3: ───────────────╰X──RY(-0.30)─╰C──RY(0.10)────────────────┤


#### New transform for transpilation ⚙️

• Added a swap based transpiler transform. (#2118)

The transpile function takes a quantum function and a coupling map as inputs and compiles the circuit to ensure that it can be executed on corresponding hardware. The transform can be used as a decorator in the following way:

dev = qml.device('default.qubit', wires=4)

@qml.qnode(dev)
@qml.transforms.transpile(coupling_map=[(0, 1), (1, 2), (2, 3)])
def circuit(param):
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[0, 2])
qml.CNOT(wires=[0, 3])
qml.PhaseShift(param, wires=0)
return qml.probs(wires=[0, 1, 2, 3])

>>> print(qml.draw(circuit)(0.3))
0: ─╭C───────╭C──────────╭C──Rϕ(0.30)─┤ ╭Probs
1: ─╰X─╭SWAP─╰X────╭SWAP─╰X───────────┤ ├Probs
2: ────╰SWAP─╭SWAP─╰SWAP──────────────┤ ├Probs
3: ──────────╰SWAP────────────────────┤ ╰Probs


### Improvements

• QuantumTape objects are now iterable, allowing iteration over the contained operations and measurements. (#2342)

with qml.tape.QuantumTape() as tape:
qml.RX(0.432, wires=0)
qml.RY(0.543, wires=0)
qml.CNOT(wires=[0, 'a'])
qml.RX(0.133, wires='a')
qml.expval(qml.PauliZ(wires=[0]))


Given a QuantumTape object the underlying quantum circuit can be iterated over using a for loop:

>>> for op in tape:
...     print(op)
RX(0.432, wires=[0])
RY(0.543, wires=[0])
CNOT(wires=[0, 'a'])
RX(0.133, wires=['a'])
expval(PauliZ(wires=[0]))


Indexing into the circuit is also allowed via tape[i]:

>>> tape[0]
RX(0.432, wires=[0])


A tape object can also be converted to a sequence (e.g., to a list) of operations and measurements:

>>> list(tape)
[RX(0.432, wires=[0]),
RY(0.543, wires=[0]),
CNOT(wires=[0, 'a']),
RX(0.133, wires=['a']),
expval(PauliZ(wires=[0]))]

• Added the QuantumTape.shape method and QuantumTape.numeric_type attribute to allow extracting information about the shape and numeric type of the output returned by a quantum tape after execution. (#2044)

dev = qml.device("default.qubit", wires=2)
a = np.array([0.1, 0.2, 0.3])

def func(a):
qml.RY(a[0], wires=0)
qml.RX(a[1], wires=0)
qml.RY(a[2], wires=0)

with qml.tape.QuantumTape() as tape:
func(a)
qml.state()

>>> tape.shape(dev)
(1, 4)
>>> tape.numeric_type
complex

• Defined a MeasurementProcess.shape method and a MeasurementProcess.numeric_type attribute to allow extracting information about the shape and numeric type of results obtained when evaluating QNodes using the specific measurement process. (#2044)

• The parameter-shift Hessian can now be computed for arbitrary operations that support the general parameter-shift rule for gradients, using qml.gradients.param_shift_hessian (#2319)

Multiple ways to obtain the gradient recipe are supported, in the following order of preference:

• A custom grad_recipe. It is iterated to obtain the shift rule for the second-order derivatives in the diagonal entries of the Hessian.

• Custom parameter_frequencies. The second-order shift rule can directly be computed using them.

• An operation’s generator. Its eigenvalues will be used to obtain parameter_frequencies, if they are not given explicitly for an operation.

• The strategy for expanding a circuit can now be specified with the qml.specs transform, for example to calculate the specifications of the circuit that will actually be executed by the device (expansion_strategy="device"). (#2395)

• The default.qubit and default.mixed devices now skip over identity operators instead of performing matrix multiplication with the identity. (#2356) (#2365)

• The function qml.eigvals is modified to use the efficient scipy.sparse.linalg.eigsh method for obtaining the eigenvalues of a SparseHamiltonian. This scipy method is called to compute $$k$$ eigenvalues of a sparse $$N \times N$$ matrix if k is smaller than $$N-1$$. If a larger $$k$$ is requested, the dense matrix representation of the Hamiltonian is constructed and the regular qml.math.linalg.eigvalsh is applied. (#2333)

• The function qml.ctrl was given the optional argument control_values=None. If overridden, control_values takes an integer or a list of integers corresponding to the binary value that each control value should take. The same change is reflected in ControlledOperation. Control values of 0 are implemented by qml.PauliX applied before and after the controlled operation (#2288)

• Operators now have a has_matrix property denoting whether or not the operator defines a matrix. (#2331) (#2476)

• Circuit cutting now performs expansion to search for wire cuts in contained operations or tapes. (#2340)

• The qml.draw and qml.draw_mpl transforms are now located in the drawer module. They can still be accessed via the top-level qml namespace. (#2396)

• Raise a warning where caching produces identical shot noise on execution results with finite shots. (#2478)

### Deprecations

• The ObservableReturnTypes Sample, Variance, Expectation, Probability, State, and MidMeasure have been moved to measurements from operation. (#2329) (#2481)

### Breaking changes

• The caching ability of devices has been removed. Using the caching on the QNode level is the recommended alternative going forward. (#2443)

One way for replicating the removed QubitDevice caching behaviour is by creating a cache object (e.g., a dictionary) and passing it to the QNode:

n_wires = 4
wires = range(n_wires)

dev = qml.device('default.qubit', wires=n_wires)

cache = {}

@qml.qnode(dev, diff_method='parameter-shift', cache=cache)
def expval_circuit(params):
qml.templates.BasicEntanglerLayers(params, wires=wires, rotation=qml.RX)
return qml.expval(qml.PauliZ(0) @ qml.PauliY(1) @ qml.PauliX(2) @ qml.PauliZ(3))

shape = qml.templates.BasicEntanglerLayers.shape(5, n_wires)
params = np.random.random(shape)

>>> expval_circuit(params)
>>> dev.num_executions
1
>>> expval_circuit(params)
>>> dev.num_executions
1

• The qml.finite_diff function has been removed. Please use qml.gradients.finite_diff to compute the gradient of tapes of QNodes. Otherwise, manual implementation is required. (#2464)

• The get_unitary_matrix transform has been removed, please use qml.matrix instead. (#2457)

• The update_stepsize method has been removed from GradientDescentOptimizer and its child optimizers. The stepsize property can be interacted with directly instead. (#2370)

• Most optimizers no longer flatten and unflatten arguments during computation. Due to this change, user provided gradient functions must return the same shape as qml.grad. (#2381)

• The old circuit text drawing infrastructure has been removed. (#2310)

• RepresentationResolver was replaced by the Operator.label method.

• qml.drawer.CircuitDrawer was replaced by qml.drawer.tape_text.

• qml.drawer.CHARSETS was removed because unicode is assumed to be accessible.

• Grid and qml.drawer.drawable_grid were removed because the custom data class was replaced by list of sets of operators or measurements.

• qml.transforms.draw_old was replaced by qml.draw.

• qml.CircuitGraph.greedy_layers was deleted, as it was no longer needed by the circuit drawer and did not seem to have uses outside of that situation.

• qml.CircuitGraph.draw was deleted, as we draw tapes instead.

• The tape method qml.tape.QuantumTape.draw now simply calls qml.drawer.tape_text.

• In the new pathway, the charset keyword was deleted, the max_length keyword defaults to 100, and the decimals and show_matrices keywords were added.

• The deprecated QNode, available via qml.qnode_old.QNode, has been removed. Please transition to using the standard qml.QNode. (#2336) (#2337) (#2338)

In addition, several other components which powered the deprecated QNode have been removed:

• The deprecated, non-batch compatible interfaces, have been removed.

• The deprecated tape subclasses QubitParamShiftTape, JacobianTape, CVParamShiftTape, and ReversibleTape have been removed.

• The deprecated tape execution method tape.execute(device) has been removed. Please use qml.execute([tape], device) instead. (#2339)

### Bug fixes

• Fixed a bug in the qml.PauliRot operation, where computing the generator was not taking into account the operation wires. (#2466)

• Fixed a bug where non-trainable arguments were shifted in the NesterovMomentumOptimizer if a trainable argument was after it in the argument list. (#2466)

• Fixed a bug with @jax.jit for grad when diff_method="adjoint" and mode="backward". (#2460)

• Fixed a bug where qml.DiagonalQubitUnitary did not support @jax.jit and @tf.function. (#2445)

• Fixed a bug in the qml.PauliRot operation, where computing the generator was not taking into account the operation wires. (#2442)

• Fixed a bug with the padding capability of AmplitudeEmbedding where the inputs are on the GPU. (#2431)

• Fixed a bug by adding a comprehensible error message for calling qml.probs without passing wires or an observable. (#2438)

• The behaviour of qml.about() was modified to avoid warnings being emitted due to legacy behaviour of pip. (#2422)

• Fixed a bug where observables were not considered when determining the use of the jax-jit interface. (#2427) (#2474)

• Fixed a bug where computing statistics for a relatively few number of shots (e.g., shots=10), an error arose due to indexing into an array using a Array. (#2427)

• PennyLane Lightning version in Docker container is pulled from latest wheel-builds. (#2416)

• Optimizers only consider a variable trainable if they have requires_grad = True. (#2381)

• Fixed a bug with qml.expval, qml.var, qml.state and qml.probs (when qml.probs is the only measurement) where the dtype specified on the device did not match the dtype of the QNode output. (#2367)

• Fixed a bug where the output shapes from batch transforms are inconsistent with the QNode output shape. (#2215)

• Fixed a bug caused by the squeezing in qml.gradients.param_shift_hessian. (#2215)

• Fixed a bug in which the expval/var of a Tensor(Observable) would depend on the order in which the observable is defined: (#2276)

>>> @qml.qnode(dev)
... def circ(op):
...   qml.RX(0.12, wires=0)
...   qml.RX(1.34, wires=1)
...   qml.RX(3.67, wires=2)
...   return qml.expval(op)
>>> op1 = qml.Identity(wires=0) @ qml.Identity(wires=1) @ qml.PauliZ(wires=2)
>>> op2 = qml.PauliZ(wires=2) @ qml.Identity(wires=0) @ qml.Identity(wires=1)
>>> print(circ(op1), circ(op2))
-0.8636111153905662 -0.8636111153905662

• Fixed a bug where qml.hf.transform_hf() would fail due to missing wires in the qubit operator that is prepared for tapering the HF state. (#2441)

• Fixed a bug with custom device defined jacobians not being returned properly. (#2485)

### Documentation

• The sections on adding operator and observable support in the “How to add a plugin” section of the plugins page have been updated. (#2389)

• The missing arXiv reference in the LieAlgebra optimizer has been fixed. (#2325)

### Contributors

This release contains contributions from (in alphabetical order):

Karim Alaa El-Din, Guillermo Alonso-Linaje, Juan Miguel Arrazola, Ali Asadi, Utkarsh Azad, Sam Banning, Thomas Bromley, Alain Delgado, Isaac De Vlugt, Olivia Di Matteo, Amintor Dusko, Anthony Hayes, David Ittah, Josh Izaac, Soran Jahangiri, Nathan Killoran, Christina Lee, Angus Lowe, Romain Moyard, Zeyue Niu, Matthew Silverman, Lee James O’Riordan, Maria Schuld, Jay Soni, Antal Száva, Maurice Weber, David Wierichs.

orphan

## Release 0.22.2¶

### Bug fixes

• Most compilation transforms, and relevant subroutines, have been updated to support just-in-time compilation with jax.jit. This fix was intended to be included in v0.22.0, but due to a bug was incomplete. (#2397)

### Documentation

• The documentation run has been updated to require jinja2==3.0.3 due to an issue that arises with jinja2 v3.1.0 and sphinx v3.5.3. (#2378)

### Contributors

This release contains contributions from (in alphabetical order):

Olivia Di Matteo, Christina Lee, Romain Moyard, Antal Száva.

orphan

## Release 0.22.1¶

### Bug fixes

• Fixes cases with qml.measure where unexpected operations were added to the circuit. (#2328)

### Contributors

This release contains contributions from (in alphabetical order):

Guillermo Alonso-Linaje, Antal Száva.

orphan

## Release 0.22.0¶

### New features since last release

#### Quantum circuit cutting ✂️

• You can now run N-wire circuits on devices with fewer than N wires, by strategically placing WireCut operations that allow their circuit to be partitioned into smaller fragments, at a cost of needing to perform a greater number of device executions. Circuit cutting is enabled by decorating a QNode with the @qml.cut_circuit transform. (#2107) (#2124) (#2153) (#2165) (#2158) (#2169) (#2192) (#2216) (#2168) (#2223) (#2231) (#2234) (#2244) (#2251) (#2265) (#2254) (#2260) (#2257) (#2279)

The example below shows how a three-wire circuit can be run on a two-wire device:

dev = qml.device("default.qubit", wires=2)

@qml.cut_circuit
@qml.qnode(dev)
def circuit(x):
qml.RX(x, wires=0)
qml.RY(0.9, wires=1)
qml.RX(0.3, wires=2)

qml.CZ(wires=[0, 1])
qml.RY(-0.4, wires=0)

qml.WireCut(wires=1)

qml.CZ(wires=[1, 2])

return qml.expval(qml.grouping.string_to_pauli_word("ZZZ"))


Instead of executing the circuit directly, it will be partitioned into smaller fragments according to the WireCut locations, and each fragment executed multiple times. Combining the results of the fragment executions will recover the expected output of the original uncut circuit.

>>> x = np.array(0.531, requires_grad=True)
>>> circuit(0.531)
0.47165198882111165


Circuit cutting support is also differentiable:

>>> qml.grad(circuit)(x)
-0.276982865449393


For more details on circuit cutting, check out the qml.cut_circuit documentation page or Peng et. al.

#### Conditional operations: quantum teleportation unlocked 🔓🌀

• Support for mid-circuit measurements and conditional operations has been added, to enable use cases like quantum teleportation, quantum error correction and quantum error mitigation. (#2211) (#2236) (#2275)

Two new functions have been added to support this capability:

• qml.measure() places mid-circuit measurements in the middle of a quantum function.

• qml.cond() allows operations and quantum functions to be conditioned on the result of a previous measurement.

For example, the code below shows how to teleport a qubit from wire 0 to wire 2:

dev = qml.device("default.qubit", wires=3)
input_state = np.array([1, -1], requires_grad=False) / np.sqrt(2)

@qml.qnode(dev)
def teleport(state):
# Prepare input state
qml.QubitStateVector(state, wires=0)

# Prepare Bell state
qml.CNOT(wires=[1, 2])

# Apply gates
qml.CNOT(wires=[0, 1])

# Measure first two wires
m1 = qml.measure(0)
m2 = qml.measure(1)

# Condition final wire on results
qml.cond(m2 == 1, qml.PauliX)(wires=2)
qml.cond(m1 == 1, qml.PauliZ)(wires=2)

# Return state on final wire
return qml.density_matrix(wires=2)


We can double-check that the qubit has been teleported by computing the overlap between the input state and the resulting state on wire 2:

>>> output_state = teleport(input_state)
>>> output_state
tensor([[ 0.5+0.j, -0.5+0.j],
>>> input_state.conj() @ output_state @ input_state


For a full description of new capabilities, refer to the Mid-circuit measurements and conditional operations section in the documentation.

• Train mid-circuit measurements by deferring them, via the new @qml.defer_measurements transform. (#2211) (#2236) (#2275)

If a device doesn’t natively support mid-circuit measurements, the @qml.defer_measurements transform can be applied to the QNode to transform the QNode into one with terminal measurements and controlled operations:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
@qml.defer_measurements
def circuit(x):

m = qml.measure(0)

def op_if_true():
return qml.RX(x**2, wires=1)

def op_if_false():
return qml.RY(x, wires=1)

qml.cond(m==1, op_if_true, op_if_false)()

return qml.expval(qml.PauliZ(1))

>>> x = np.array(0.7, requires_grad=True)
>>> print(qml.draw(circuit, expansion_strategy="device")(x))
0: ──H─╭C─────────X─╭C─────────X─┤
1: ────╰RX(0.49)────╰RY(0.70)────┤  <Z>
>>> circuit(x)


Deferring mid-circuit measurements also enables differentiation:

>>> qml.grad(circuit)(x)
-0.651546965338656


#### Debug with mid-circuit quantum snapshots 📷

• A new operation qml.Snapshot has been added to assist in debugging quantum functions. (#2233) (#2289) (#2291) (#2315)

qml.Snapshot saves the internal state of devices at arbitrary points of execution.

Currently supported devices include:

• default.qubit: each snapshot saves the quantum state vector

• default.mixed: each snapshot saves the density matrix

• default.gaussian: each snapshot saves the covariance matrix and vector of means

During normal execution, the snapshots are ignored:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev, interface=None)
def circuit():
qml.Snapshot()
qml.Snapshot("very_important_state")
qml.CNOT(wires=[0, 1])
qml.Snapshot()
return qml.expval(qml.PauliX(0))


However, when using the qml.snapshots transform, intermediate device states will be stored and returned alongside the results.

>>> qml.snapshots(circuit)()
{0: array([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]),
'very_important_state': array([0.70710678+0.j, 0.        +0.j, 0.70710678+0.j, 0.        +0.j]),
2: array([0.70710678+0.j, 0.        +0.j, 0.        +0.j, 0.70710678+0.j]),
'execution_results': array(0.)}


#### Batch embedding and state preparation data 📦

• Added the @qml.batch_input transform to enable batching non-trainable gate parameters. In addition, the qml.qnn.KerasLayer class has been updated to natively support batched training data. (#2069)

As with other transforms, @qml.batch_input can be used to decorate QNodes:

dev = qml.device("default.qubit", wires=2, shots=None)

@qml.batch_input(argnum=0)
@qml.qnode(dev, diff_method="parameter-shift", interface="tf")
def circuit(inputs, weights):
# add a batch dimension to the embedding data
qml.AngleEmbedding(inputs, wires=range(2), rotation="Y")
qml.RY(weights[0], wires=0)
qml.RY(weights[1], wires=1)
return qml.expval(qml.PauliZ(1))


Batched input parameters can then be passed during QNode evaluation:

>>> x = tf.random.uniform((10, 2), 0, 1)
>>> w = tf.random.uniform((2,), 0, 1)
>>> circuit(x, w)
<tf.Tensor: shape=(10,), dtype=float64, numpy=
array([0.46230079, 0.73971315, 0.95666004, 0.5355225 , 0.66180948,
0.44519553, 0.93874261, 0.9483197 , 0.78737918, 0.90866411])>


#### Even more mighty quantum transforms 🐛➡🦋

• New functions and transforms of operators have been added:

• qml.matrix() for computing the matrix representation of one or more unitary operators. (#2241)

• qml.eigvals() for computing the eigenvalues of one or more operators. (#2248)

• qml.generator() for computing the generator of a single-parameter unitary operation. (#2256)

All operator transforms can be used on instantiated operators,

>>> op = qml.RX(0.54, wires=0)
>>> qml.matrix(op)
[[0.9637709+0.j         0.       -0.26673144j]
[0.       -0.26673144j 0.9637709+0.j        ]]


Operator transforms can also be used in a functional form:

>>> x = torch.tensor(0.6, requires_grad=True)
>>> matrix_fn = qml.matrix(qml.RX)
>>> matrix_fn(x, wires=[0])
tensor([[0.9553+0.0000j, 0.0000-0.2955j],


In its functional form, it is fully differentiable with respect to gate arguments:

>>> loss = torch.real(torch.trace(matrix_fn(x, wires=0)))
>>> loss.backward()
tensor(-0.2955)


Some operator transform can also act on multiple operations, by passing quantum functions or tapes:

>>> def circuit(theta):
...     qml.RX(theta, wires=1)
...     qml.PauliZ(wires=0)
>>> qml.matrix(circuit)(np.pi / 4)
array([[ 0.92387953+0.j,  0.+0.j ,  0.-0.38268343j,  0.+0.j],
[ 0.+0.j,  -0.92387953+0.j,  0.+0.j,  0. +0.38268343j],
[ 0. -0.38268343j,  0.+0.j,  0.92387953+0.j,  0.+0.j],
[ 0.+0.j,  0.+0.38268343j,  0.+0.j,  -0.92387953+0.j]])

• A new transform has been added to construct the pairwise-commutation directed acyclic graph (DAG) representation of a quantum circuit. (#1712)

In the DAG, each node represents a quantum operation, and edges represent non-commutation between two operations.

This transform takes into account that not all operations can be moved next to each other by pairwise commutation:

>>> def circuit(x, y, z):
...     qml.RX(x, wires=0)
...     qml.RX(y, wires=0)
...     qml.CNOT(wires=[1, 2])
...     qml.RY(y, wires=1)
...     qml.CRZ(z, wires=[2, 0])
...     qml.RY(-y, wires=1)
...     return qml.expval(qml.PauliZ(0))
>>> dag_fn = qml.commutation_dag(circuit)
>>> dag = dag_fn(np.pi / 4, np.pi / 3, np.pi / 2)


Nodes in the commutation DAG can be accessed via the get_nodes() method, returning a list of the form (ID, CommutationDAGNode):

>>> nodes = dag.get_nodes()
>>> nodes
NodeDataView({0: <pennylane.transforms.commutation_dag.CommutationDAGNode object at 0x7f461c4bb580>, ...}, data='node')


Specific nodes in the commutation DAG can be accessed via the get_node() method:

>>> second_node = dag.get_node(2)
>>> second_node
<pennylane.transforms.commutation_dag.CommutationDAGNode object at 0x136f8c4c0>
>>> second_node.op
CNOT(wires=[1, 2])
>>> second_node.successors
[3, 4, 5, 6]
>>> second_node.predecessors
[]


### Improvements

• The text-based drawer accessed via qml.draw() has been optimized and improved. (#2128) (#2198)

The new drawer has:

• a decimals keyword for controlling parameter rounding

• a show_matrices keyword for controlling display of matrices

• a different algorithm for determining positions

• deprecation of the charset keyword

@qml.qnode(qml.device('lightning.qubit', wires=2))
def circuit(a, w):
qml.CRX(a, wires=[0, 1])
qml.Rot(*w, wires=[1])
qml.CRX(-a, wires=[0, 1])
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

>>> print(qml.draw(circuit, decimals=2)(a=2.3, w=[1.2, 3.2, 0.7]))
0: ──H─╭C─────────────────────────────╭C─────────┤ ╭<[email protected]>
1: ────╰RX(2.30)──Rot(1.20,3.20,0.70)─╰RX(-2.30)─┤ ╰<[email protected]>

• The frequencies of gate parameters are now accessible as an operation property and can be used for circuit analysis, optimization via the RotosolveOptimizer and differentiation with the parameter-shift rule (including the general shift rule). (#2180) (#2182) (#2227)

>>> op = qml.CRot(0.4, 0.1, 0.3, wires=[0, 1])
>>> op.parameter_frequencies
[(0.5, 1.0), (0.5, 1.0), (0.5, 1.0)]


When using qml.gradients.param_shift, either a custom grad_recipe or the parameter frequencies are used to obtain the shift rule for the operation, in that order of preference.

See Vidal and Theis (2018) and Wierichs et al. (2021) for theoretical background information on the general parameter-shift rule.

• No two-term parameter-shift rule is assumed anymore by default. (#2227)

Previously, operations marked for analytic differentiation that did not provide a generator, parameter_frequencies or a custom grad_recipe were assumed to satisfy the two-term shift rule. This now has to be made explicit for custom operations by adding any of the above attributes.

• Most compilation transforms, and relevant subroutines, have been updated to support just-in-time compilation with jax.jit. (#1894)

• The qml.draw_mpl transform supports a expansion_strategy keyword argument. (#2271)

• The qml.gradients module has been streamlined and special-purpose functions moved closer to their use cases, while preserving existing behaviour. (#2200)

• Added a new partition_pauli_group function to the grouping module for efficiently measuring the N-qubit Pauli group with 3 ** N qubit-wise commuting terms. (#2185)

• The Operator class has undergone a major refactor with the following changes:

• Matrices: the static method Operator.compute_matrices() defines the matrix representation of the operator, and the function qml.matrix(op) computes this for a given instance. (#1996)

• Eigvals: the static method Operator.compute_eigvals() defines the matrix representation of the operator, and the function qml.eigvals(op) computes this for a given instance. (#2048)

• Decompositions: the static method Operator.compute_decomposition() defines the matrix representation of the operator, and the method op.decomposition() computes this for a given instance. (#2024) (#2053)

• Sparse matrices: the static method Operator.compute_sparse_matrix() defines the sparse matrix representation of the operator, and the method op.sparse_matrix() computes this for a given instance. (#2050)

• Linear combinations of operators: The static method compute_terms(), used for representing the linear combination of coefficients and operators representing the operator, has been added. The method op.terms() computes this for a given instance. Currently, only the Hamiltonian class overwrites compute_terms() to store coefficients and operators. The Hamiltonian.terms property hence becomes a proper method called by Hamiltonian.terms(). (#2036)

• Diagonalization: The diagonalizing_gates() representation has been moved to the highest-level Operator class and is therefore available to all subclasses. A condition qml.operation.defines_diagonalizing_gates has been added, which can be used in tape contexts without queueing. In addition, a static compute_diagonalizing_gates method has been added, which is called by default in diagonalizing_gates(). (#1985) (#1993)

• Error handling has been improved for Operator representations. Custom errors subclassing OperatorPropertyUndefined are raised if a representation has not been defined. This replaces the NotImplementedError and allows finer control for developers. (#2064) (#2287)

• A Operator.hyperparameters attribute, used for storing operation parameters that are never trainable, has been added to the operator class. (#2017)

• The string_for_inverse attribute is removed. (#2021)

• The expand() method was moved from the Operation class to the main Operator class. (#2053) (#2239)

### Deprecations

• There are several important changes when creating custom operations: (#2214) (#2227) (#2030) (#2061)

• The Operator.matrix method has been deprecated and Operator.compute_matrix should be defined instead. Operator matrices should be accessed using qml.matrix(op). If you were previously defining the class method Operator._matrix(), this is a a breaking change — please update your operation to instead overwrite Operator.compute_matrix.

• The Operator.decomposition method has been deprecated and Operator.compute_decomposition should be defined instead. Operator decompositions should be accessed using Operator.decomposition().

• The Operator.eigvals method has been deprecated and Operator.compute_eigvals should be defined instead. Operator eigenvalues should be accessed using qml.eigvals(op).

• The Operator.generator property is now a method, and should return an operator instance representing the generator. Note that unlike the other representations above, this is a breaking change. Operator generators should be accessed using qml.generator(op).

• The Operation.get_parameter_shift method has been deprecated and will be removed in a future release.

Instead, the functionalities for general parameter-shift rules in the qml.gradients module should be used, together with the operation attributes parameter_frequencies or grad_recipe.

• Executing tapes using tape.execute(dev) is deprecated. Please use the qml.execute([tape], dev) function instead. (#2306)

• The subclasses of the quantum tape, including JacobianTape, QubitParamShiftTape, CVParamShiftTape, and ReversibleTape are deprecated. Instead of calling JacobianTape.jacobian() and JacobianTape.hessian(), please use a standard QuantumTape, and apply gradient transforms using the qml.gradients module. (#2306)

• qml.transforms.get_unitary_matrix() has been deprecated and will be removed in a future release. For extracting matrices of operations and quantum functions, please use qml.matrix(). (#2248)

• The qml.finite_diff() function has been deprecated and will be removed in an upcoming release. Instead, qml.gradients.finite_diff() can be used to compute purely quantum gradients (that is, gradients of tapes or QNode). (#2212)

• The MultiControlledX operation now accepts a single wires keyword argument for both control_wires and wires. The single wires keyword should be all the control wires followed by a single target wire. (#2121) (#2278)

### Breaking changes

• The representation of an operator as a matrix has been overhauled. (#1996)

The “canonical matrix”, which is independent of wires, is now defined in the static method compute_matrix() instead of _matrix. By default, this method is assumed to take all parameters and non-trainable hyperparameters that define the operation.

>>> qml.RX.compute_matrix(0.5)
[[0.96891242+0.j         0.        -0.24740396j]
[0.        -0.24740396j 0.96891242+0.j        ]]


If no canonical matrix is specified for a gate, compute_matrix() raises a MatrixUndefinedError.

• The generator property has been updated to an instance method, Operator.generator(). It now returns an instantiated operation, representing the generator of the instantiated operator. (#2030) (#2061)

Various operators have been updated to specify the generator as either an Observable, Tensor, Hamiltonian, SparseHamiltonian, or Hermitian operator.

In addition, qml.generator(operation) has been added to aid in retrieving generator representations of operators.

• The argument wires in heisenberg_obs, heisenberg_expand and heisenberg_tr was renamed to wire_order to be consistent with other matrix representations. (#2051)

• The property kraus_matrices has been changed to a method, and _kraus_matrices renamed to compute_kraus_matrices, which is now a static method. (#2055)

• The pennylane.measure module has been renamed to pennylane.measurements. (#2236)

### Bug fixes

• The basis property of qml.SWAP was set to "X", which is incorrect; it is now set to None. (#2287)

• The qml.RandomLayers template now decomposes when the weights are a list of lists. (#2266)

• The qml.QubitUnitary operation now supports just-in-time compilation using JAX. (#2249)

• Fixes a bug in the JAX interface where Array objects were not being converted to NumPy arrays before executing an external device. (#2255)

• The qml.ctrl transform now works correctly with gradient transforms such as the parameter-shift rule. (#2238)

• Fixes a bug in which passing required arguments into operations as keyword arguments would throw an error because the documented call signature didn’t match the function definition. (#1976)

• The operation OrbitalRotation previously was wrongfully registered to satisfy the four-term parameter shift rule. The correct eight-term rule will now be used when using the parameter-shift rule. (#2180)

• Fixes a bug where qml.gradients.param_shift_hessian would produce an error whenever all elements of the Hessian are known in advance to be 0. (#2299)

### Documentation

• The developer guide on adding templates and the architecture overview were rewritten to reflect the past and planned changes of the operator refactor. (#2066)

• Links to the Strawberry Fields documentation for information on the CV model. (#2259)

• Fixes the documentation example for qml.QFT. (#2232)

• Fixes the documentation example for using qml.sample with jax.jit. (#2196)

• The qml.numpy subpackage is now included in the PennyLane API documentation. (#2179)

• Improves the documentation of RotosolveOptimizer regarding the usage of the passed substep_optimizer and its keyword arguments. (#2160)

• Ensures that signatures of @qml.qfunc_transform decorated functions display correctly in the docs. (#2286)

• Docstring examples now display using the updated text-based circuit drawer. (#2252)

• Add docstring to OrbitalRotation.grad_recipe. (#2193)

### Contributors

This release contains contributions from (in alphabetical order):

Catalina Albornoz, Jack Y. Araz, Juan Miguel Arrazola, Ali Asadi, Utkarsh Azad, Sam Banning, Thomas Bromley, Olivia Di Matteo, Christian Gogolin, Diego Guala, Anthony Hayes, David Ittah, Josh Izaac, Soran Jahangiri, Nathan Killoran, Christina Lee, Angus Lowe, Maria Fernanda Morris, Romain Moyard, Zeyue Niu, Lee James O’Riordan, Chae-Yeun Park, Maria Schuld, Jay Soni, Antal Száva, David Wierichs.

orphan

## Release 0.21.0¶

### New features since last release

#### Reduce qubit requirements of simulating Hamiltonians ⚛️

• Functions for tapering qubits based on molecular symmetries have been added, following results from Setia et al. (#1966) (#1974) (#2041) (#2042)

With this functionality, a molecular Hamiltonian and the corresponding Hartree-Fock (HF) state can be transformed to a new Hamiltonian and HF state that acts on a reduced number of qubits, respectively.

# molecular geometry
symbols = ["He", "H"]
geometry = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.4588684632]])
mol = qml.hf.Molecule(symbols, geometry, charge=1)

# generate the qubit Hamiltonian
H = qml.hf.generate_hamiltonian(mol)(geometry)

# determine Hamiltonian symmetries
generators, paulix_ops = qml.hf.generate_symmetries(H, len(H.wires))
opt_sector = qml.hf.optimal_sector(H, generators, mol.n_electrons)

# taper the Hamiltonian
H_tapered = qml.hf.transform_hamiltonian(H, generators, paulix_ops, opt_sector)


We can compare the number of qubits required by the original Hamiltonian and the tapered Hamiltonian:

>>> len(H.wires)
4
>>> len(H_tapered.wires)
2


For quantum chemistry algorithms, the Hartree-Fock state can also be tapered:

n_elec = mol.n_electrons
n_qubits = mol.n_orbitals * 2

hf_tapered = qml.hf.transform_hf(
generators, paulix_ops, opt_sector, n_elec, n_qubits
)

>>> hf_tapered


#### New tensor network templates 🪢

• Quantum circuits with the shape of a matrix product state tensor network can now be easily implemented using the new qml.MPS template, based on the work arXiv:1803.11537. (#1871)

def block(weights, wires):
qml.CNOT(wires=[wires[0], wires[1]])
qml.RY(weights[0], wires=wires[0])
qml.RY(weights[1], wires=wires[1])

n_wires = 4
n_block_wires = 2
n_params_block = 2
template_weights = np.array([[0.1, -0.3], [0.4, 0.2], [-0.15, 0.5]], requires_grad=True)

dev = qml.device("default.qubit", wires=range(n_wires))

@qml.qnode(dev)
def circuit(weights):
qml.MPS(range(n_wires), n_block_wires, block, n_params_block, weights)
return qml.expval(qml.PauliZ(wires=n_wires - 1))


The resulting circuit is:

>>> print(qml.draw(circuit, expansion_strategy="device")(template_weights))
0: ──╭C──RY(0.1)───────────────────────────────┤
1: ──╰X──RY(-0.3)──╭C──RY(0.4)─────────────────┤
2: ────────────────╰X──RY(0.2)──╭C──RY(-0.15)──┤
3: ─────────────────────────────╰X──RY(0.5)────┤ ⟨Z⟩

• Added a template for tree tensor networks, qml.TTN. (#2043)

def block(weights, wires):
qml.CNOT(wires=[wires[0], wires[1]])
qml.RY(weights[0], wires=wires[0])
qml.RY(weights[1], wires=wires[1])

n_wires = 4
n_block_wires = 2
n_params_block = 2
n_blocks = qml.MPS.get_n_blocks(range(n_wires), n_block_wires)
template_weights = [[0.1, -0.3]] * n_blocks

dev = qml.device("default.qubit", wires=range(n_wires))

@qml.qnode(dev)
def circuit(template_weights):
qml.TTN(range(n_wires), n_block_wires, block, n_params_block, template_weights)
return qml.expval(qml.PauliZ(wires=n_wires - 1))


The resulting circuit is:

>>> print(qml.draw(circuit, expansion_strategy="device")(template_weights))
0: ──╭C──RY(0.1)─────────────────┤
1: ──╰X──RY(-0.3)──╭C──RY(0.1)───┤
2: ──╭C──RY(0.1)───│─────────────┤
3: ──╰X──RY(-0.3)──╰X──RY(-0.3)──┤ ⟨Z⟩


#### Generalized RotosolveOptmizer 📉

• The RotosolveOptimizer has been generalized to arbitrary frequency spectra in the cost function. Also note the changes in behaviour listed under Breaking changes. (#2081)

Previously, the RotosolveOptimizer only supported variational circuits using special gates such as single-qubit Pauli rotations. Now, circuits with arbitrary gates are supported natively without decomposition, as long as the frequencies of the gate parameters are known. This new generalization extends the Rotosolve optimization method to a larger class of circuits, and can reduce the cost of the optimization compared to decomposing all gates to single-qubit rotations.

Consider the QNode

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def qnode(x, Y):
qml.RX(2.5 * x, wires=0)
qml.CNOT(wires=[0, 1])
qml.RZ(0.3 * Y[0], wires=0)
qml.CRY(1.1 * Y[1], wires=[1, 0])
return qml.expval(qml.PauliX(0) @ qml.PauliZ(1))



Its frequency spectra can be easily obtained via qml.fourier.qnode_spectrum:

>>> spectra = qml.fourier.qnode_spectrum(qnode)(x, Y)
>>> spectra
{'x': {(): [-2.5, 0.0, 2.5]},
'Y': {(0,): [-0.3, 0.0, 0.3], (1,): [-1.1, -0.55, 0.0, 0.55, 1.1]}}


We may then initialize the RotosolveOptimizer and minimize the QNode cost function by providing this information about the frequency spectra. We also compare the cost at each step to the initial cost.

>>> cost_init = qnode(x, Y)
>>> opt = qml.RotosolveOptimizer()
>>> for _ in range(2):
...     x, Y = opt.step(qnode, x, Y, spectra=spectra)
...     print(f"New cost: {np.round(qnode(x, Y), 3)}; Initial cost: {np.round(cost_init, 3)}")
New cost: 0.0; Initial cost: 0.706
New cost: -1.0; Initial cost: 0.706


The optimization with RotosolveOptimizer is performed in substeps. The minimal cost of these substeps can be retrieved by setting full_output=True.

>>> x = np.array(0.8, requires_grad=True)
>>> Y = np.array([-0.2, 1.5], requires_grad=True)
>>> opt = qml.RotosolveOptimizer()
>>> for _ in range(2):
...     (x, Y), history = opt.step(qnode, x, Y, spectra=spectra, full_output=True)
...     print(f"New cost: {np.round(qnode(x, Y), 3)} reached via substeps {np.round(history, 3)}")
New cost: 0.0 reached via substeps [-0.  0.  0.]
New cost: -1.0 reached via substeps [-1. -1. -1.]


However, note that these intermediate minimal values are evaluations of the reconstructions that Rotosolve creates and uses internally for the optimization, and not of the original objective function. For noisy cost functions, these intermediate evaluations may differ significantly from evaluations of the original cost function.

#### Improved JAX support 💻

• The JAX interface now supports evaluating vector-valued QNodes. (#2110)

Vector-valued QNodes include those with:

• qml.probs;

• qml.state;

• qml.sample or

• multiple qml.expval / qml.var measurements.

Consider a QNode that returns basis-state probabilities:

dev = qml.device('default.qubit', wires=2)
x = jnp.array(0.543)
y = jnp.array(-0.654)

@qml.qnode(dev, diff_method="parameter-shift", interface="jax")
def circuit(x, y):
qml.RX(x, wires=[0])
qml.RY(y, wires=[1])
qml.CNOT(wires=[0, 1])
return qml.probs(wires=[1])


The QNode can be evaluated and its jacobian can be computed:

>>> circuit(x, y)
Array([0.8397495 , 0.16025047], dtype=float32)
>>> jax.jacobian(circuit, argnums=[0, 1])(x, y)
(Array([-0.2050439,  0.2050439], dtype=float32, weak_type=True),
Array([ 0.26043, -0.26043], dtype=float32, weak_type=True))


Note that jax.jit is not yet supported for vector-valued QNodes.

#### Speedier quantum natural gradient ⚡

• A new function for computing the metric tensor on simulators, qml.adjoint_metric_tensor, has been added, that uses classically efficient methods to massively improve performance. (#1992)

This method, detailed in Jones (2020), computes the metric tensor using four copies of the state vector and a number of operations that scales quadratically in the number of trainable parameters.

Note that as it makes use of state cloning, it is inherently classical and can only be used with statevector simulators and shots=None.

It is particularly useful for larger circuits for which backpropagation requires inconvenient or even unfeasible amounts of storage, but is slower. Furthermore, the adjoint method is only available for analytic computation, not for measurements simulation with shots!=None.

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev)
def circuit(x, y):
qml.Rot(*x[0], wires=0)
qml.Rot(*x[1], wires=1)
qml.Rot(*x[2], wires=2)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
qml.CNOT(wires=[2, 0])
qml.RY(y[0], wires=0)
qml.RY(y[1], wires=1)
qml.RY(y[0], wires=2)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1)), qml.expval(qml.PauliY(1))

x = np.array([[0.2, 0.4, -0.1], [-2.1, 0.5, -0.2], [0.1, 0.7, -0.6]], requires_grad=False)

>>> qml.adjoint_metric_tensor(circuit)(x, y)
tensor([[ 0.25495723, -0.07086695],


Computational cost

The adjoint method uses $$2P^2+4P+1$$ gates and state cloning operations if the circuit is composed only of trainable gates, where $$P$$ is the number of trainable operations. If non-trainable gates are included, each of them is applied about $$n^2-n$$ times, where $$n$$ is the number of trainable operations that follow after the respective non-trainable operation in the circuit. This means that non-trainable gates later in the circuit are executed less often, making the adjoint method a bit cheaper if such gates appear later. The adjoint method requires memory for 4 independent state vectors, which corresponds roughly to storing a state vector of a system with 2 additional qubits.

#### Compute the Hessian on hardware ⬆️

• A new gradient transform qml.gradients.param_shift_hessian has been added to directly compute the Hessian (2nd order partial derivative matrix) of QNodes on hardware. (#1884)

The function generates parameter-shifted tapes which allow the Hessian to be computed analytically on hardware and software devices. Compared to using an auto-differentiation framework to compute the Hessian via parameter shifts, this function will use fewer device invocations and can be used to inspect the parameter-shifted “Hessian tapes” directly. The function remains fully differentiable on all supported PennyLane interfaces.

Additionally, the parameter-shift Hessian comes with a new batch transform decorator @qml.gradients.hessian_transform, which can be used to create custom Hessian functions.

The following code demonstrates how to use the parameter-shift Hessian:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(x):
qml.RX(x[0], wires=0)
qml.RY(x[1], wires=0)
return qml.expval(qml.PauliZ(0))


>>> hessian
tensor([[-0.97517033,  0.01983384],


### Improvements

• The qml.transforms.insert transform now supports adding operation after or before certain specific gates. (#1980)

• Added a modified version of the simplify function to the hf module. (#2103)

This function combines redundant terms in a Hamiltonian and eliminates terms with a coefficient smaller than a cutoff value. The new function makes construction of molecular Hamiltonians more efficient. For LiH, as an example, the time to construct the Hamiltonian is reduced roughly by a factor of 20.

• The QAOA module now accepts both NetworkX and RetworkX graphs as function inputs. (#1791)

• The CircuitGraph, used to represent circuits via directed acyclic graphs, now uses RetworkX for its internal representation. This results in significant speedup for algorithms that rely on a directed acyclic graph representation. (#1791)

• For subclasses of Operator where the number of parameters is known before instantiation, the num_params is reverted back to being a static property. This allows to programmatically know the number of parameters before an operator is instantiated without changing the user interface. A test was added to ensure that different ways of defining num_params work as expected. (#2101) (#2135)

• A WireCut operator has been added for manual wire cut placement when constructing a QNode. (#2093)

• The new function qml.drawer.tape_text produces a string drawing of a tape. This function differs in implementation and minor stylistic details from the old string circuit drawing infrastructure. (#1885)

• The RotosolveOptimizer now raises an error if no trainable arguments are detected, instead of silently skipping update steps for all arguments. (#2109)

• The function qml.math.safe_squeeze is introduced and gradient_transform allows for QNode argument axes of size 1. (#2080)

qml.math.safe_squeeze wraps qml.math.squeeze, with slight modifications:

• When provided the axis keyword argument, axes that do not have size 1 will be ignored, instead of raising an error.

• The keyword argument exclude_axis allows to explicitly exclude axes from the squeezing.

• The adjoint transform now raises and error whenever the object it is applied to is not callable. (#2060)

An example is a list of operations to which one might apply qml.adjoint:

dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit_wrong(params):
# Note the difference:                  v                         v
return qml.state()

@qml.qnode(dev)
def circuit_correct(params):
# Note the difference:                  v                         v
return qml.state()

params = list(range(1, 3))


Evaluating circuit_wrong(params) now raises a ValueError and if we apply qml.adjoint correctly, we get

>>> circuit_correct(params)
[ 0.47415988+0.j          0.         0.73846026j  0.         0.25903472j
-0.40342268+0.j        ]

• A precision argument has been added to the tape’s to_openqasm function to control the precision of parameters. (#2071)

• Interferometer now has a shape method. (#1946)

• The Barrier and Identity operations now support the adjoint method. (#2062) (#2063)

• qml.BasisStatePreparation now supports the batch_params decorator. (#2091)

• Added a new multi_dispatch decorator that helps ease the definition of new functions inside PennyLane. The decorator is used throughout the math module, demonstrating use cases. (#2082) (#2096)

We can decorate a function, indicating the arguments that are tensors handled by the interface:

>>> @qml.math.multi_dispatch(argnum=[0, 1])
... def some_function(tensor1, tensor2, option, like):
...     # the interface string is stored in like.
...     ...


Previously, this was done using the private utility function _multi_dispatch.

>>> def some_function(tensor1, tensor2, option):
...     interface = qml.math._multi_dispatch([tensor1, tensor2])
...     ...

• The IsingZZ gate was added to the diagonal_in_z_basis attribute. For this an explicit _eigvals method was added. (#2113)

• The IsingXX, IsingYY and IsingZZ gates were added to the composable_rotations attribute. (#2113)

### Breaking changes

• QNode arguments will no longer be considered trainable by default when using the Autograd interface. In order to obtain derivatives with respect to a parameter, it should be instantiated via PennyLane’s NumPy wrapper using the requires_grad=True attribute. The previous behaviour was deprecated in version v0.19.0 of PennyLane. (#2116) (#2125) (#2139) (#2148) (#2156)

from pennylane import numpy as np

@qml.qnode(qml.device("default.qubit", wires=2))
def circuit(x):
...



For the qml.grad and qml.jacobian functions, trainability can alternatively be indicated via the argnum keyword:

import numpy as np

@qml.qnode(qml.device("default.qubit", wires=2))
def circuit(hyperparam, param):
...

x = np.array([0.1, 0.2])

• qml.jacobian now follows a different convention regarding its output shape. (#2059)

Previously, qml.jacobian would attempt to stack the Jacobian for multiple QNode arguments, which succeeded whenever the arguments have the same shape. In this case, the stacked Jacobian would also be transposed, leading to the output shape (*reverse_QNode_args_shape, *reverse_output_shape, num_QNode_args)

If no stacking and transposing occurs, the output shape instead is a tuple where each entry corresponds to one QNode argument and has the shape (*output_shape, *QNode_arg_shape).

This breaking change alters the behaviour in the first case and removes the attempt to stack and transpose, so that the output always has the shape of the second type.

Note that the behaviour is unchanged — that is, the Jacobian tuple is unpacked into a single Jacobian — if argnum=None and there is only one QNode argument with respect to which the differentiation takes place, or if an integer is provided as argnum.

A workaround that allowed qml.jacobian to differentiate multiple QNode arguments will no longer support higher-order derivatives. In such cases, combining multiple arguments into a single array is recommended.

• qml.metric_tensor, qml.adjoint_metric_tensor and qml.transforms.classical_jacobian now follow a different convention regarding their output shape when being used with the Autograd interface (#2059)

See the previous entry for details. This breaking change immediately follows from the change in qml.jacobian whenever hybrid=True is used in the above methods.

• The behaviour of RotosolveOptimizer has been changed regarding its keyword arguments. (#2081)

The keyword arguments optimizer and optimizer_kwargs for the RotosolveOptimizer have been renamed to substep_optimizer and substep_kwargs, respectively. Furthermore they have been moved from step and step_and_cost to the initialization __init__.

The keyword argument num_freqs has been renamed to nums_frequency and is expected to take a different shape now: Previously, it was expected to be an int or a list of entries, with each entry in turn being either an int or a list of int entries. Now the expected structure is a nested dictionary, matching the formatting expected by qml.fourier.reconstruct This also matches the expected formatting of the new keyword arguments spectra and shifts.

For more details, see the RotosolveOptimizer documentation.

### Deprecations

• Deprecates the caching ability provided by QubitDevice. (#2154)

Going forward, the preferred way is to use the caching abilities of the QNode:

dev = qml.device("default.qubit", wires=2)

cache = {}

@qml.qnode(dev, diff_method='parameter-shift', cache=cache)
def circuit():
qml.RY(0.345, wires=0)
return qml.expval(qml.PauliZ(0))

>>> for _ in range(10):
...    circuit()
>>> dev.num_executions
1


### Bug fixes

• Fixes a bug where an incorrect number of executions are recorded by a QNode using a custom cache with diff_method="backprop". (#2171)

• Fixes a bug where the default.qubit.jax device can’t be used with diff_method=None and jitting. (#2136)

• Fixes a bug where the Torch interface was not properly unwrapping Torch tensors to NumPy arrays before executing gradient tapes on devices. (#2117)

• Fixes a bug for the TensorFlow interface where the dtype of input tensors was not cast. (#2120)

• Fixes a bug where batch transformed QNodes would fail to apply batch transforms provided by the underlying device. (#2111)

• An error is now raised during QNode creation if backpropagation is requested on a device with finite shots specified. (#2114)

• Pytest now ignores any DeprecationWarning raised within autograd’s numpy_wrapper module. Other assorted minor test warnings are fixed. (#2007)

• Fixes a bug where the QNode was not correctly diagonalizing qubit-wise commuting observables. (#2097)

• Fixes a bug in gradient_transform where the hybrid differentiation of circuits with a single parametrized gate failed and QNode argument axes of size 1 where removed from the output gradient. (#2080)

• The available diff_method options for QNodes has been corrected in both the error messages and the documentation. (#2078)

• Fixes a bug in DefaultQubit where the second derivative of QNodes at positions corresponding to vanishing state vector amplitudes is wrong. (#2057)

• Fixes a bug where PennyLane didn’t require v0.20.0 of PennyLane-Lightning, but raised an error with versions of Lightning earlier than v0.20.0 due to the new batch execution pipeline. (#2033)

• Fixes a bug in classical_jacobian when used with Torch, where the Jacobian of the preprocessing was also computed for non-trainable parameters. (#2020)

• Fixes a bug in queueing of the two_qubit_decomposition method that originally led to circuits with >3 two-qubit unitaries failing when passed through the unitary_to_rot optimization transform. (#2015)

• Fixes a bug which allows using jax.jit to be compatible with circuits which return qml.probs when the default.qubit.jax is provided with a custom shot vector. (#2028)

• Updated the adjoint() method for non-parametric qubit operations to solve a bug where repeated adjoint() calls don’t return the correct operator. (#2133)

• Fixed a bug in insert() which prevented operations that inherited from multiple classes to be inserted. (#2172)

### Documentation

• Fixes an error in the signs of equations in the DoubleExcitation page. (#2072)

• Extends the interfaces description page to explicitly mention device compatibility. (#2031)

### Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Ali Asadi, Utkarsh Azad, Sam Banning, Thomas Bromley, Esther Cruz, Olivia Di Matteo, Christian Gogolin, Diego Guala, Anthony Hayes, David Ittah, Josh Izaac, Soran Jahangiri, Edward Jiang, Ankit Khandelwal, Nathan Killoran, Korbinian Kottmann, Christina Lee, Romain Moyard, Lee James O’Riordan, Maria Schuld, Jay Soni, Antal Száva, David Wierichs, Shaoming Zhang.

orphan

## Release 0.20.0¶

### New features since last release

#### Shiny new circuit drawer!🎨🖌️

• PennyLane now supports drawing a QNode with matplotlib! (#1803) (#1811) (#1931) (#1954)

dev = qml.device("default.qubit", wires=4)

@qml.qnode(dev)
def circuit(x, z):
qml.QFT(wires=(0,1,2,3))
qml.Toffoli(wires=(0,1,2))
qml.CSWAP(wires=(0,2,3))
qml.RX(x, wires=0)
qml.CRZ(z, wires=(3,0))
return qml.expval(qml.PauliZ(0))
fig, ax = qml.draw_mpl(circuit)(1.2345, 1.2345)
fig.show()


#### New and improved quantum-aware optimizers

• Added qml.LieAlgebraOptimizer, a new quantum-aware Lie Algebra optimizer that allows one to perform gradient descent on the special unitary group. (#1911)

dev = qml.device("default.qubit", wires=2)
H = -1.0 * qml.PauliX(0) - qml.PauliZ(1) - qml.PauliY(0) @ qml.PauliX(1)

@qml.qnode(dev)
def circuit():
qml.RX(0.1, wires=[0])
qml.RY(0.5, wires=[1])
qml.CNOT(wires=[0,1])
qml.RY(0.6, wires=[0])
return qml.expval(H)
opt = qml.LieAlgebraOptimizer(circuit=circuit, stepsize=0.1)


Note that, unlike other optimizers, the LieAlgebraOptimizer accepts a QNode with no parameters, and instead grows the circuit by appending operations during the optimization:

>>> circuit()
>>> circuit1, cost = opt.step_and_cost()
>>> circuit1()


For more details, see the LieAlgebraOptimizer documentation.

• The qml.metric_tensor transform can now be used to compute the full tensor, beyond the block diagonal approximation. (#1725)

This is performed using Hadamard tests, and requires an additional wire on the device to execute the circuits produced by the transform, as compared to the number of wires required by the original circuit. The transform defaults to computing the full tensor, which can be controlled by the approx keyword argument.

As an example, consider the QNode

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev)
def circuit(weights):
qml.RX(weights[0], wires=0)
qml.RY(weights[1], wires=0)
qml.CNOT(wires=[0, 1])
qml.RZ(weights[2], wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

weights = np.array([0.2, 1.2, -0.9], requires_grad=True)


Then we can compute the (block) diagonal metric tensor as before, now using the approx="block-diag" keyword:

>>> qml.metric_tensor(circuit, approx="block-diag")(weights)
[[0.25       0.         0.        ]
[0.         0.24013262 0.        ]
[0.         0.         0.21846983]]


Instead, we now can also compute the full metric tensor, using Hadamard tests on the additional wire of the device:

>>> qml.metric_tensor(circuit)(weights)
[[ 0.25        0.         -0.23300977]
[ 0.          0.24013262  0.01763859]
[-0.23300977  0.01763859  0.21846983]]


#### Faster performance with optimized quantum workflows

• The QNode has been re-written to support batch execution across the board, custom gradients, better decomposition strategies, and higher-order derivatives. (#1807) (#1969)

• Internally, if multiple circuits are generated for simultaneous execution, they will be packaged into a single job for execution on the device. This can lead to significant performance improvement when executing the QNode on remote quantum hardware or simulator devices with parallelization capabilities.

• Custom gradient transforms can be specified as the differentiation method:

@qml.gradients.gradient_transform
...
return tapes, processing_fn

def circuit():


For breaking changes related to the use of the new QNode, refer to the Breaking Changes section.

Note that the old QNode remains accessible at @qml.qnode_old.qnode, however this will be removed in the next release.

• Custom decompositions can now be applied to operations at the device level. (#1900)

For example, suppose we would like to implement the following QNode:

def circuit(weights):
qml.BasicEntanglerLayers(weights, wires=[0, 1, 2])
return qml.expval(qml.PauliZ(0))

original_dev = qml.device("default.qubit", wires=3)
original_qnode = qml.QNode(circuit, original_dev)

>>> weights = np.array([[0.4, 0.5, 0.6]])
>>> print(qml.draw(original_qnode, expansion_strategy="device")(weights))
0: ──RX(0.4)──╭C──────╭X──┤ ⟨Z⟩
1: ──RX(0.5)──╰X──╭C──│───┤
2: ──RX(0.6)──────╰X──╰C──┤


Now, let’s swap out the decomposition of the CNOT gate into CZ and Hadamard, and furthermore the decomposition of Hadamard into RZ and RY rather than the decomposition already available in PennyLane. We define the two decompositions like so, and pass them to a device:

def custom_cnot(wires):
return [
qml.CZ(wires=[wires[0], wires[1]]),
]

return [
qml.RZ(np.pi, wires=wires),
qml.RY(np.pi / 2, wires=wires)
]

# Can pass the operation itself, or a string

decomp_dev = qml.device("default.qubit", wires=3, custom_decomps=custom_decomps)
decomp_qnode = qml.QNode(circuit, decomp_dev)


Now when we draw or run a QNode on this device, the gates will be expanded according to our specifications:

>>> print(qml.draw(decomp_qnode, expansion_strategy="device")(weights))
0: ──RX(0.4)──────────────────────╭C──RZ(3.14)──RY(1.57)──────────────────────────╭Z──RZ(3.14)──RY(1.57)──┤ ⟨Z⟩
1: ──RX(0.5)──RZ(3.14)──RY(1.57)──╰Z──RZ(3.14)──RY(1.57)──╭C──────────────────────│───────────────────────┤
2: ──RX(0.6)──RZ(3.14)──RY(1.57)──────────────────────────╰Z──RZ(3.14)──RY(1.57)──╰C──────────────────────┤


A separate context manager, set_decomposition, has also been implemented to enable application of custom decompositions on devices that have already been created.

>>> with qml.transforms.set_decomposition(custom_decomps, original_dev):
...     print(qml.draw(original_qnode, expansion_strategy="device")(weights))
0: ──RX(0.4)──────────────────────╭C──RZ(3.14)──RY(1.57)──────────────────────────╭Z──RZ(3.14)──RY(1.57)──┤ ⟨Z⟩
1: ──RX(0.5)──RZ(3.14)──RY(1.57)──╰Z──RZ(3.14)──RY(1.57)──╭C──────────────────────│───────────────────────┤
2: ──RX(0.6)──RZ(3.14)──RY(1.57)──────────────────────────╰Z──RZ(3.14)──RY(1.57)──╰C──────────────────────┤

• Given an operator of the form $$U=e^{iHt}$$, where $$H$$ has commuting terms and known eigenvalues, qml.gradients.generate_shift_rule computes the generalized parameter shift rules for determining the gradient of the expectation value $$f(t) = \langle 0|U(t)^\dagger \hat{O} U(t)|0\rangle$$ on hardware. (#1788) (#1932)

Given

$H = \sum_i a_i h_i,$

where the eigenvalues of $$H$$ are known and all $$h_i$$ commute, we can compute the frequencies (the unique positive differences of any two eigenvalues) using qml.gradients.eigvals_to_frequencies.

qml.gradients.generate_shift_rule can then be used to compute the parameter shift rules to compute $$f'(t)$$ using 2R shifted cost function evaluations. This becomes cheaper than the standard application of the chain rule and two-term shift rule when R is less than the number of Pauli words in the generator.

For example, consider the case where $$H$$ has eigenspectrum (-1, 0, 1):

>>> frequencies = qml.gradients.eigvals_to_frequencies((-1, 0, 1))
>>> frequencies
(1, 2)
>>> coeffs
array([ 0.85355339, -0.85355339, -0.14644661,  0.14644661])
>>> shifts
array([ 0.78539816, -0.78539816,  2.35619449, -2.35619449])


As we can see, generate_shift_rule returns four coefficients $$c_i$$ and shifts $$s_i$$ corresponding to a four term parameter shift rule. The gradient can then be reconstructed via:

$\frac{\partial}{\partial\phi}f = \sum_{i} c_i f(\phi + s_i),$

where $$f(\phi) = \langle 0|U(\phi)^\dagger \hat{O} U(\phi)|0\rangle$$ for some observable $$\hat{O}$$ and the unitary $$U(\phi)=e^{iH\phi}$$.

#### Support for TensorFlow AutoGraph mode with quantum hardware

• It is now possible to use TensorFlow’s AutoGraph mode with QNodes on all devices and with arbitrary differentiation methods. Previously, AutoGraph mode only support diff_method="backprop". This will result in significantly more performant model execution, at the cost of a more expensive initial compilation. (#1866)

Use AutoGraph to convert your QNodes or cost functions into TensorFlow graphs by decorating them with @tf.function:

dev = qml.device("lightning.qubit", wires=2)

def circuit(x):
qml.RX(x[0], wires=0)
qml.RY(x[1], wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1)), qml.expval(qml.PauliZ(0))

@tf.function
def cost(x):
return tf.reduce_sum(circuit(x))

x = tf.Variable([0.5, 0.7], dtype=tf.float64)

loss = cost(x)



The initial execution may take slightly longer than when executing the circuit in eager mode; this is because TensorFlow is tracing the function to create the graph. Subsequent executions will be much more performant.

Note that using AutoGraph with backprop-enabled devices, such as default.qubit, will yield the best performance.

For more details, please see the TensorFlow AutoGraph documentation.

#### Characterize your quantum models with classical QNode reconstruction

• The qml.fourier.reconstruct function is added. It can be used to reconstruct QNodes outputting expectation values along a specified parameter dimension, with a minimal number of calls to the original QNode. The returned reconstruction is exact and purely classical, and can be evaluated without any quantum executions. (#1864)

The reconstruction technique differs for functions with equidistant frequencies that are reconstructed using the function value at equidistant sampling points, and for functions with arbitrary frequencies reconstructed using arbitrary sampling points.

As an example, consider the following QNode:

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(x, Y, f=1.0):
qml.RX(f * x, wires=0)
qml.RY(Y[0], wires=0)
qml.RY(Y[1], wires=1)
qml.CNOT(wires=[0, 1])
qml.RY(3 * Y[1], wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))


It has three variational parameters overall: A scalar input x and an array-valued input Y with two entries. Additionally, we can tune the dependence on x with the frequency f. We then can reconstruct the QNode output function with respect to x via

>>> x = 0.3
>>> Y = np.array([0.1, -0.9])
>>> rec = qml.fourier.reconstruct(circuit, ids="x", nums_frequency={"x": {0: 1}})(x, Y)
>>> rec
{'x': {0: <function pennylane.fourier.reconstruct._reconstruct_equ.<locals>._reconstruction(x)>}}


As we can see, we get a nested dictionary in the format of the input nums_frequency with functions as values. These functions are simple float-to-float callables:

>>> univariate = rec["x"][0]
>>> univariate(x)
-0.880208251507


For more details on usage, reconstruction cost and differentiability support, please see the fourier.reconstruct docstring.

#### State-of-the-art operations and templates

• A circuit template for time evolution under a commuting Hamiltonian utilizing generalized parameter shift rules for cost function gradients is available as qml.CommutingEvolution. (#1788)

If the template is handed a frequency spectrum during its instantiation, then generate_shift_rule is internally called to obtain the general parameter shift rules with respect to CommutingEvolution‘s $$t$$ parameter, otherwise the shift rule for a decomposition of CommutingEvolution will be used.

The template can be initialized within QNode as:

import pennylane as qml

n_wires = 2
dev = qml.device('default.qubit', wires=n_wires)

coeffs = [1, -1]
obs = [qml.PauliX(0) @ qml.PauliY(1), qml.PauliY(0) @ qml.PauliX(1)]
hamiltonian = qml.Hamiltonian(coeffs, obs)
frequencies = (2,4)

@qml.qnode(dev)
def circuit(time):
qml.PauliX(0)
qml.CommutingEvolution(hamiltonian, time, frequencies)
return qml.expval(qml.PauliZ(0))


Note that there is no internal validation that 1) the input qml.Hamiltonian is fully commuting and 2) the eigenvalue frequency spectrum is correct, since these checks become prohibitively expensive for large Hamiltonians.

• The qml.Barrier() operator has been added. With it we can separate blocks in compilation or use it as a visual tool. (#1844)

• Added the identity observable to be an operator. Now we can explicitly call the identity operation on our quantum circuits for both qubit and CV devices. (#1829)

• Added the qml.QubitDensityMatrix initialization gate for mixed state simulation. (#1850)

• A thermal relaxation channel is added to the Noisy channels. The channel description can be found on the supplementary information of Quantum classifier with tailored quantum kernels. (#1766)

• Added a new qml.PauliError channel that allows the application of an arbitrary number of Pauli operators on an arbitrary number of wires. (#1781)

#### Manipulate QNodes to your ❤️s content with new transforms

• The merge_amplitude_embedding transformation has been created to automatically merge all gates of this type into one. (#1933)

from pennylane.transforms import merge_amplitude_embedding

dev = qml.device("default.qubit", wires = 3)

@qml.qnode(dev)
@merge_amplitude_embedding
def qfunc():
qml.AmplitudeEmbedding([0,1,0,0], wires = [0,1])
qml.AmplitudeEmbedding([0,1], wires = 2)
return qml.expval(qml.PauliZ(wires = 0))

>>> print(qml.draw(qnode)())
0: ──╭AmplitudeEmbedding(M0)──┤ ⟨Z⟩
1: ──├AmplitudeEmbedding(M0)──┤
2: ──╰AmplitudeEmbedding(M0)──┤
M0 =
[0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]

• The undo_swaps transformation has been created to automatically remove all swaps of a circuit. (#1960)

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
@qml.transforms.undo_swaps
def qfunc():
qml.PauliX(wires=1)
qml.SWAP(wires=[0,1])
qml.SWAP(wires=[0,2])
qml.PauliY(wires=0)
return qml.expval(qml.PauliZ(0))

>>> print(qml.draw(qfunc)())
0: ──Y──┤ ⟨Z⟩
1: ──H──┤
2: ──X──┤


### Improvements

• Added functions for computing the values of atomic and molecular orbitals at a given position. (#1867)

The functions atomic_orbital and molecular_orbital can be used, as shown in the following codeblock, to evaluate the orbitals. By generating values of the orbitals at different positions, one can plot the spatial shape of a desired orbital.

symbols  = ['H', 'H']
geometry = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]], requires_grad = False)
mol = hf.Molecule(symbols, geometry)
hf.generate_scf(mol)()

ao = mol.atomic_orbital(0)
mo = mol.molecular_orbital(1)

>>> print(ao(0.0, 0.0, 0.0))
>>> print(mo(0.0, 0.0, 0.0))
0.6282468778183719
0.018251285973461928

• Added support for Python 3.10. (#1964)

• The execution of QNodes that have

• multiple return types;

• a return type other than Variance and Expectation

now raises a descriptive error message when using the JAX interface. (#2011)

• The PennyLane qchem package is now lazily imported; it will only be imported the first time it is accessed. (#1962)

• qml.math.scatter_element_add now supports adding multiple values at multiple indices with a single function call, in all interfaces (#1864)

For example, we may set five values of a three-dimensional tensor in the following way:

>>> X = tf.zeros((3, 2, 9), dtype=tf.float64)
>>> indices = [(0, 0, 1, 2, 2), (0, 0, 0, 0, 1), (1, 3, 8, 6, 7)]
>>> values = [1 * i for i in range(1,6)]
<tf.Tensor: shape=(3, 2, 9), dtype=float64, numpy=
array([[[0., 1., 0., 2., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0.]],

[[0., 0., 0., 0., 0., 0., 0., 0., 3.],
[0., 0., 0., 0., 0., 0., 0., 0., 0.]],

[[0., 0., 0., 0., 0., 0., 4., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 5., 0.]]])>

• All instances of str.format have been replace with f-strings. (#1970)

• Tests do not loop over automatically imported and instantiated operations any more, which was opaque and created unnecessarily many tests. (#1895)

• A decompose() method has been added to the Operator class such that we can obtain (and queue) decompositions directly from instances of operations. (#1873)

>>> op = qml.PhaseShift(0.3, wires=0)
>>> op.decompose()
[RZ(0.3, wires=[0])]

• qml.circuit_drawer.tape_mpl produces a matplotlib figure and axes given a tape. (#1787)

• The AngleEmbedding, BasicEntanglerLayers and MottonenStatePreparation templates now support parameters with batch dimension when using the @qml.batch_params decorator. (#1812) (#1883) (#1893)

• qml.draw now supports a max_length argument to help prevent text overflows when printing circuits. (#1892)

• Identity operation is now part of both the ops.qubit and ops.cv modules. (#1956)

### Breaking changes

• The QNode has been re-written to support batch execution across the board, custom gradients, better decomposition strategies, and higher-order derivatives. (#1807) (#1969)

• Arbitrary $$n$$-th order derivatives are supported on hardware using gradient transforms such as the parameter-shift rule. To specify that an $$n$$-th order derivative of a QNode will be computed, the max_diff argument should be set. By default, this is set to 1 (first-order derivatives only). Increasing this value allows for higher order derivatives to be extracted, at the cost of additional (classical) computational overhead during the backwards pass.

• When decomposing the circuit, the default decomposition strategy expansion_strategy="gradient" will prioritize decompositions that result in the smallest number of parametrized operations required to satisfy the differentiation method. While this may lead to a slight increase in classical processing, it significantly reduces the number of circuit evaluations needed to compute gradients of complicated unitaries.

To return to the old behaviour, expansion_strategy="device" can be specified.

Note that the old QNode remains accessible at @qml.qnode_old.qnode, however this will be removed in the next release.

• Certain features deprecated in v0.19.0 have been removed: (#1981) (#1963)

• The qml.template decorator (use a  QuantumTape <https://pennylane.readthedocs.io/en/stable/code/api/pennylane.tape.QuantumTape.html>_ as a context manager to record operations and its operations attribute to return them, see the linked page for examples);

• The default.tensor and default.tensor.tf experimental devices;

• The qml.fourier.spectrum function (use the qml.fourier.circuit_spectrum or qml.fourier.qnode_spectrum functions instead);

• The diag_approx keyword argument of qml.metric_tensor and qml.QNGOptimizer (pass approx='diag' instead).

• The default behaviour of the qml.metric_tensor transform has been modified. By default, the full metric tensor is computed, leading to higher cost than the previous default of computing the block diagonal only. At the same time, the Hadamard tests for the full metric tensor require an additional wire on the device, so that

>>> qml.metric_tensor(some_qnode)(weights)


will revert back to the block diagonal restriction and raise a warning if the used device does not have an additional wire. (#1725)

• The circuit_drawer module has been renamed drawer. (#1949)

• The par_domain attribute in the operator class has been removed. (#1907)

• The mutable keyword argument has been removed from the QNode, due to underlying bugs that result in incorrect results being returned from immutable QNodes. This functionality will return in an upcoming release. (#1807)

• The reversible QNode differentiation method has been removed; the adjoint differentiation method is preferred instead (diff_method='adjoint'). (#1807)

• QuantumTape.trainable_params now is a list instead of a set. This means that tape.trainable_params will return a list unlike before, but setting the trainable_params with a set works exactly as before. (#1904)

• The num_params attribute in the operator class is now dynamic. This makes it easier to define operator subclasses with a flexible number of parameters. (#1898) (#1909)

• The static method decomposition(), formerly in the Operation class, has been moved to the base Operator class. (#1873)

• DiagonalOperation is not a separate subclass any more. (#1889)

Instead, devices can check for the diagonal property using attributes:

from pennylane.ops.qubit.attributes import diagonal_in_z_basis

if op in diagonal_in_z_basis:
# do something


Custom operations can be added to this attribute at runtime via diagonal_in_z_basis.add("MyCustomOp").

### Bug fixes

• Fixes a bug with qml.probs when using default.qubit.jax. (#1998)

• Fixes a bug where output tensors of a QNode would always be put on the default GPU with default.qubit.torch. (#1982)

• Device test suite doesn’t use empty circuits so that it can also test the IonQ plugin, and it checks if operations are supported in more places. (#1979)

• Fixes a bug where the metric tensor was computed incorrectly when using gates with gate.inverse=True. (#1987)

• Corrects the documentation of qml.transforms.classical_jacobian for the Autograd interface (and improves test coverage). (#1978)

• Fixes a bug where differentiating a QNode with qml.state using the JAX interface raised an error. (#1906)

• Fixes a bug with the adjoint of qml.QFT. (#1955)

• Fixes a bug where the ApproxTimeEvolution template was not correctly computing the operation wires from the input Hamiltonian. This did not affect computation with the ApproxTimeEvolution template, but did cause circuit drawing to fail. (#1952)

• Fixes a bug where the classical preprocessing Jacobian computed by qml.transforms.classical_jacobian with JAX returned a reduced submatrix of the Jacobian. (#1948)

• Fixes a bug where the operations are not accessed in the correct order in qml.fourier.qnode_spectrum, leading to wrong outputs. (#1935)

• Fixes several Pylint errors. (#1951)

• Fixes a bug where the device test suite wasn’t testing certain operations. (#1943)

• Fixes a bug where batch transforms would mutate a QNodes execution options. (#1934)

• qml.draw now supports arbitrary templates with matrix parameters. (#1917)

• QuantumTape.trainable_params now is a list instead of a set, making it more stable in very rare edge cases. (#1904)

• ExpvalCost now returns corrects results shape when optimize=True with shots batch. (#1897)

• qml.circuit_drawer.MPLDrawer was slightly modified to work with matplotlib version 3.5. (#1899)

• qml.CSWAP and qml.CRot now define control_wires, and qml.SWAP returns the default empty wires object. (#1830)

• The requires_grad attribute of qml.numpy.tensor objects is now preserved when pickling/unpickling the object. (#1856)

• Device tests no longer throw warnings about the requires_grad attribute of variational parameters. (#1913)

• AdamOptimizer and AdagradOptimizer had small fixes to their optimization step updates. (#1929)

• Fixes a bug where differentiating a QNode with multiple array arguments via qml.gradients.param_shift throws an error. (#1989)

• AmplitudeEmbedding template no longer produces a ComplexWarning when the features parameter is batched and provided as a 2D array. (#1990)

• qml.circuit_drawer.CircuitDrawer no longer produces an error when attempting to draw tapes inside of circuits (e.g. from decomposition of an operation or manual placement). (#1994)

• Fixes a bug where using SciPy sparse matrices with the new QNode could lead to a warning being raised about prioritizing the TensorFlow and PyTorch interfaces. (#2001)

• Fixed a bug where the QueueContext was not empty when first importing PennyLane. (#1957)

• Fixed circuit drawing problem with Interferometer and CVNeuralNet. (#1953)

### Documentation

• Added examples in documentation for some operations. (#1902)

• Improves the Developer’s Guide Testing document. (#1896)

• Added documentation examples for AngleEmbedding, BasisEmbedding, StronglyEntanglingLayers, SqueezingEmbedding, DisplacementEmbedding, MottonenStatePreparation and Interferometer. (#1910) (#1908) (#1912) (#1920) (#1936) (#1937)

### Contributors

This release contains contributions from (in alphabetical order):

Catalina Albornoz, Guillermo Alonso-Linaje, Juan Miguel Arrazola, Ali Asadi, Utkarsh Azad, Samuel Banning, Benjamin Cordier, Alain Delgado, Olivia Di Matteo, Anthony Hayes, David Ittah, Josh Izaac, Soran Jahangiri, Jalani Kanem, Ankit Khandelwal, Nathan Killoran, Shumpei Kobayashi, Robert Lang, Christina Lee, Cedric Lin, Alejandro Montanez, Romain Moyard, Lee James O’Riordan, Chae-Yeun Park, Isidor Schoch, Maria Schuld, Jay Soni, Antal Száva, Rodrigo Vargas, David Wierichs, Roeland Wiersema, Moritz Willmann.

orphan

## Release 0.19.1¶

### Bug fixes

• Fixes several bugs when using parametric operations with the default.qubit.tensor device on GPU. The device takes the torch_device argument once again to allow running non-parametric QNodes on the GPU. (#1927)

• Fixes a bug where using JAX’s jit function on certain QNodes that contain the qml.QubitStateVector operation raised an error with earlier JAX versions (e.g., jax==0.2.10 and jaxlib==0.1.64). (#1924)

### Contributors

This release contains contributions from (in alphabetical order):

Josh Izaac, Christina Lee, Romain Moyard, Lee James O’Riordan, Antal Száva.

orphan

## Release 0.19.0¶

### New features since last release

#### Differentiable Hartree-Fock solver

• A differentiable Hartree-Fock (HF) solver has been added. It can be used to construct molecular Hamiltonians that can be differentiated with respect to nuclear coordinates and basis-set parameters. (#1610)

The HF solver computes the integrals over basis functions, constructs the relevant matrices, and performs self-consistent-field iterations to obtain a set of optimized molecular orbital coefficients. These coefficients and the computed integrals over basis functions are used to construct the one- and two-body electron integrals in the molecular orbital basis which can be used to generate a differentiable second-quantized Hamiltonian in the fermionic and qubit basis.

The following code shows the construction of the Hamiltonian for the hydrogen molecule where the geometry of the molecule is differentiable.

symbols = ["H", "H"]
geometry = np.array([[0.0000000000, 0.0000000000, -0.6943528941],

mol = qml.hf.Molecule(symbols, geometry)
args_mol = [geometry]

hamiltonian = qml.hf.generate_hamiltonian(mol)(*args_mol)

>>> hamiltonian.coeffs
tensor([-0.09041082+0.j,  0.17220382+0.j,  0.17220382+0.j,
0.16893367+0.j,  0.04523101+0.j, -0.04523101+0.j,
-0.04523101+0.j,  0.04523101+0.j, -0.22581352+0.j,
0.12092003+0.j, -0.22581352+0.j,  0.16615103+0.j,


The generated Hamiltonian can be used in a circuit where the atomic coordinates and circuit parameters are optimized simultaneously.

symbols = ["H", "H"]
geometry = np.array([[0.0000000000, 0.0000000000, 0.0],

mol = qml.hf.Molecule(symbols, geometry)

dev = qml.device("default.qubit", wires=4)

def generate_circuit(mol):
@qml.qnode(dev)
def circuit(*args):
qml.BasisState(np.array([1, 1, 0, 0]), wires=[0, 1, 2, 3])
qml.DoubleExcitation(*args[0][0], wires=[0, 1, 2, 3])
return qml.expval(qml.hf.generate_hamiltonian(mol)(*args[1:]))
return circuit

for n in range(25):

mol = qml.hf.Molecule(symbols, geometry)
args = [params, geometry] # initial values of the differentiable parameters

g_params = qml.grad(generate_circuit(mol), argnum = 0)(*args)
params = params - 0.5 * g_params[0]

forces = qml.grad(generate_circuit(mol), argnum = 1)(*args)
geometry = geometry - 0.5 * forces

print(f'Step: {n}, Energy: {generate_circuit(mol)(*args)}, Maximum Force: {forces.max()}')


In addition, the new Hartree-Fock solver can further be used to optimize the basis set parameters. For details, please refer to the differentiable Hartree-Fock solver documentation.

#### Integration with Mitiq

• Error mitigation using the zero-noise extrapolation method is now available through the transforms.mitigate_with_zne transform. This transform can integrate with the Mitiq package for unitary folding and extrapolation functionality. (#1813)

Consider the following noisy device:

noise_strength = 0.05
dev = qml.device("default.mixed", wires=2)
dev = qml.transforms.insert(qml.AmplitudeDamping, noise_strength)(dev)


We can mitigate the effects of this noise for circuits run on this device by using the added transform:

from mitiq.zne.scaling import fold_global
from mitiq.zne.inference import RichardsonFactory

n_wires = 2
n_layers = 2

shapes = qml.SimplifiedTwoDesign.shape(n_wires, n_layers)
np.random.seed(0)
w1, w2 = [np.random.random(s) for s in shapes]

@qml.transforms.mitigate_with_zne([1, 2, 3], fold_global, RichardsonFactory.extrapolate)
@qml.beta.qnode(dev)
def circuit(w1, w2):
qml.SimplifiedTwoDesign(w1, w2, wires=range(2))
return qml.expval(qml.PauliZ(0))


Now, when we execute circuit, errors will be automatically mitigated:

>>> circuit(w1, w2)
0.19113067083636542


#### Powerful new transforms

• The unitary matrix corresponding to a quantum circuit can now be generated using the new get_unitary_matrix() transform. (#1609) (#1786)

This transform is fully differentiable across all supported PennyLane autodiff frameworks.

def circuit(theta):
qml.RX(theta, wires=1)
qml.PauliZ(wires=0)
qml.CNOT(wires=[0, 1])

>>> theta = torch.tensor(0.3, requires_grad=True)
>>> matrix = qml.transforms.get_unitary_matrix(circuit)(theta)
>>> print(matrix)
tensor([[ 0.9888+0.0000j,  0.0000+0.0000j,  0.0000-0.1494j,  0.0000+0.0000j],
[ 0.0000+0.0000j,  0.0000+0.1494j,  0.0000+0.0000j, -0.9888+0.0000j],
[ 0.0000-0.1494j,  0.0000+0.0000j,  0.9888+0.0000j,  0.0000+0.0000j],
[ 0.0000+0.0000j, -0.9888+0.0000j,  0.0000+0.0000j,  0.0000+0.1494j]],
>>> loss = torch.real(torch.trace(matrix))
>>> loss.backward()
tensor(-0.1494)

• Arbitrary two-qubit unitaries can now be decomposed into elementary gates. This functionality has been incorporated into the qml.transforms.unitary_to_rot transform, and is available separately as qml.transforms.two_qubit_decomposition. (#1552)

As an example, consider the following randomly-generated matrix and circuit that uses it:

U = np.array([
[-0.03053706-0.03662692j,  0.01313778+0.38162226j, 0.4101526 -0.81893687j, -0.03864617+0.10743148j],
[-0.17171136-0.24851809j,  0.06046239+0.1929145j, -0.04813084-0.01748555j, -0.29544883-0.88202604j],
[ 0.39634931-0.78959795j, -0.25521689-0.17045233j, -0.1391033 -0.09670952j, -0.25043606+0.18393466j],
[ 0.29599198-0.19573188j,  0.55605806+0.64025769j, 0.06140516+0.35499559j,  0.02674726+0.1563311j ]
])

dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
@qml.transforms.unitary_to_rot
def circuit(x, y):
qml.QubitUnitary(U, wires=[0, 1])
return qml.expval(qml.PauliZ(wires=0))


If we run the circuit, we can see the new decomposition:

>>> circuit(0.3, 0.4)
>>> print(qml.draw(circuit)(0.3, 0.4))
0: ──Rot(2.78, 0.242, -2.28)──╭X──RZ(0.176)───╭C─────────────╭X──Rot(-3.87, 0.321, -2.09)──┤ ⟨Z⟩
1: ──Rot(4.64, 2.69, -1.56)───╰C──RY(-0.883)──╰X──RY(-1.47)──╰C──Rot(1.68, 0.337, 0.587)───┤

• A new transform, @qml.batch_params, has been added, that makes QNodes handle a batch dimension in trainable parameters. (#1710) (#1761)

This transform will create multiple circuits, one per batch dimension. As a result, it is both simulator and hardware compatible.

@qml.batch_params
@qml.beta.qnode(dev)
def circuit(x, weights):
qml.RX(x, wires=0)
qml.RY(0.2, wires=1)
qml.templates.StronglyEntanglingLayers(weights, wires=[0, 1, 2])


The qml.batch_params decorator allows us to pass arguments x and weights that have a batch dimension. For example,

>>> batch_size = 3
>>> x = np.linspace(0.1, 0.5, batch_size)
>>> weights = np.random.random((batch_size, 10, 3, 3))


If we evaluate the QNode with these inputs, we will get an output of shape (batch_size,):

>>> circuit(x, weights)

• The insert transform has now been added, providing a way to insert single-qubit operations into a quantum circuit. The transform can apply to quantum functions, tapes, and devices. (#1795)

The following QNode can be transformed to add noise to the circuit:

dev = qml.device("default.mixed", wires=2)

@qml.qnode(dev)
@qml.transforms.insert(qml.AmplitudeDamping, 0.2, position="end")
def f(w, x, y, z):
qml.RX(w, wires=0)
qml.RY(x, wires=1)
qml.CNOT(wires=[0, 1])
qml.RY(y, wires=0)
qml.RX(z, wires=1)
return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))


Executions of this circuit will differ from the noise-free value:

>>> f(0.9, 0.4, 0.5, 0.6)
>>> print(qml.draw(f)(0.9, 0.4, 0.5, 0.6))
0: ──RX(0.9)──╭C──RY(0.5)──AmplitudeDamping(0.2)──╭┤ ⟨Z ⊗ Z⟩
1: ──RY(0.4)──╰X──RX(0.6)──AmplitudeDamping(0.2)──╰┤ ⟨Z ⊗ Z⟩

• Common tape expansion functions are now available in qml.transforms, alongside a new create_expand_fn function for easily creating expansion functions from stopping criteria. (#1734) (#1760)

create_expand_fn takes the default depth to which the expansion function should expand a tape, a stopping criterion, an optional device, and a docstring to be set for the created function. The stopping criterion must take a queuable object and return a boolean.

For example, to create an expansion function that decomposes all trainable, multi-parameter operations:

>>> stop_at = ~(qml.operation.has_multipar & qml.operation.is_trainable)
>>> expand_fn = qml.transforms.create_expand_fn(depth=5, stop_at=stop_at)


The created expansion function can be used within a custom transform. Devices can also be provided, producing expansion functions that decompose tapes to support the native gate set of the device.

#### Batch execution of circuits

• A new, experimental QNode has been added, that adds support for batch execution of circuits, custom quantum gradient support, and arbitrary order derivatives. This QNode is available via qml.beta.QNode, and @qml.beta.qnode. (#1642) (#1646) (#1651) (#1804)

It differs from the standard QNode in several ways:

• Custom gradient transforms can be specified as the differentiation method:

@qml.gradients.gradient_transform
...
return tapes, processing_fn

def circuit():

• Arbitrary $$n$$-th order derivatives are supported on hardware using gradient transforms such as the parameter-shift rule. To specify that an $$n$$-th order derivative of a QNode will be computed, the max_diff argument should be set. By default, this is set to 1 (first-order derivatives only).

• Internally, if multiple circuits are generated for execution simultaneously, they will be packaged into a single job for execution on the device. This can lead to significant performance improvement when executing the QNode on remote quantum hardware.

• When decomposing the circuit, the default decomposition strategy will prioritize decompositions that result in the smallest number of parametrized operations required to satisfy the differentiation method. Additional decompositions required to satisfy the native gate set of the quantum device will be performed later, by the device at execution time. While this may lead to a slight increase in classical processing, it significantly reduces the number of circuit evaluations needed to compute gradients of complex unitaries.

In an upcoming release, this QNode will replace the existing one. If you come across any bugs while using this QNode, please let us know via a bug report on our GitHub bug tracker.

Currently, this beta QNode does not support the following features:

• Non-mutability via the mutable keyword argument

• The reversible QNode differentiation method

• The ability to specify a dtype when using PyTorch and TensorFlow.

It is also not tested with the qml.qnn module.

#### New operations and templates

• Added a new operation OrbitalRotation, which implements the spin-adapted spatial orbital rotation gate. (#1665)

An example circuit that uses OrbitalRotation operation is:

dev = qml.device('default.qubit', wires=4)

@qml.qnode(dev)
def circuit(phi):
qml.BasisState(np.array([1, 1, 0, 0]), wires=[0, 1, 2, 3])
qml.OrbitalRotation(phi, wires=[0, 1, 2, 3])
return qml.state()


If we run this circuit, we will get the following output

>>> circuit(0.1)
array([ 0.        +0.j,  0.        +0.j,  0.        +0.j,
0.00249792+0.j,  0.        +0.j,  0.        +0.j,
-0.04991671+0.j,  0.        +0.j,  0.        +0.j,
-0.04991671+0.j,  0.        +0.j,  0.        +0.j,
0.99750208+0.j,  0.        +0.j,  0.        +0.j,
0.        +0.j])

• Added a new template GateFabric, which implements a local, expressive, quantum-number-preserving ansatz proposed by Anselmetti et al. in arXiv:2104.05692. (#1687)

An example of a circuit using GateFabric template is:

coordinates = np.array([0.0, 0.0, -0.6614, 0.0, 0.0, 0.6614])
H, qubits = qml.qchem.molecular_hamiltonian(["H", "H"], coordinates)
ref_state = qml.qchem.hf_state(electrons=2, orbitals=qubits)

dev = qml.device('default.qubit', wires=qubits)

@qml.qnode(dev)
def ansatz(weights):
qml.templates.GateFabric(weights, wires=[0,1,2,3],
init_state=ref_state, include_pi=True)
return qml.expval(H)


For more details, see the GateFabric documentation.

• Added a new template kUpCCGSD, which implements a unitary coupled cluster ansatz with generalized singles and pair doubles excitation operators, proposed by Joonho Lee et al. in arXiv:1810.02327. (#1743)

An example of a circuit using kUpCCGSD template is:

coordinates = np.array([0.0, 0.0, -0.6614, 0.0, 0.0, 0.6614])
H, qubits = qml.qchem.molecular_hamiltonian(["H", "H"], coordinates)
ref_state = qml.qchem.hf_state(electrons=2, orbitals=qubits)

dev = qml.device('default.qubit', wires=qubits)

@qml.qnode(dev)
def ansatz(weights):
qml.templates.kUpCCGSD(weights, wires=[0,1,2,3], k=0, delta_sz=0,
init_state=ref_state)
return qml.expval(H)


#### Improved utilities for quantum compilation and characterization

• The new qml.fourier.qnode_spectrum function extends the former qml.fourier.spectrum function and takes classical processing of QNode arguments into account. The frequencies are computed per (requested) QNode argument instead of per gate id. The gate ids are ignored. (#1681) (#1720)

Consider the following example, which uses non-trainable inputs x, y and z as well as trainable parameters w as arguments to the QNode.

import pennylane as qml
import numpy as np

n_qubits = 3
dev = qml.device("default.qubit", wires=n_qubits)

@qml.qnode(dev)
def circuit(x, y, z, w):
for i in range(n_qubits):
qml.RX(0.5*x[i], wires=i)
qml.Rot(w[0,i,0], w[0,i,1], w[0,i,2], wires=i)
qml.RY(2.3*y[i], wires=i)
qml.Rot(w[1,i,0], w[1,i,1], w[1,i,2], wires=i)
qml.RX(z, wires=i)
return qml.expval(qml.PauliZ(wires=0))

x = np.array([1., 2., 3.])
y = np.array([0.1, 0.3, 0.5])
z = -1.8
w = np.random.random((2, n_qubits, 3))


This circuit looks as follows:

>>> print(qml.draw(circuit)(x, y, z, w))
0: ──RX(0.5)──Rot(0.598, 0.949, 0.346)───RY(0.23)──Rot(0.693, 0.0738, 0.246)──RX(-1.8)──┤ ⟨Z⟩
1: ──RX(1)────Rot(0.0711, 0.701, 0.445)──RY(0.69)──Rot(0.32, 0.0482, 0.437)───RX(-1.8)──┤
2: ──RX(1.5)──Rot(0.401, 0.0795, 0.731)──RY(1.15)──Rot(0.756, 0.38, 0.38)─────RX(-1.8)──┤


Applying the qml.fourier.qnode_spectrum function to the circuit for the non-trainable parameters, we obtain:

>>> spec = qml.fourier.qnode_spectrum(circuit, encoding_args={"x", "y", "z"})(x, y, z, w)
>>> for inp, freqs in spec.items():
...     print(f"{inp}: {freqs}")
"x": {(0,): [-0.5, 0.0, 0.5], (1,): [-0.5, 0.0, 0.5], (2,): [-0.5, 0.0, 0.5]}
"y": {(0,): [-2.3, 0.0, 2.3], (1,): [-2.3, 0.0, 2.3], (2,): [-2.3, 0.0, 2.3]}
"z": {(): [-3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0]}


We can see that all three parameters in the QNode arguments x and y contribute the spectrum of a Pauli rotation [-1.0, 0.0, 1.0], rescaled with the prefactor of the respective parameter in the circuit. The three RX rotations using the parameter z accumulate, yielding a more complex frequency spectrum.

For details on how to control for which parameters the spectrum is computed, a comparison to qml.fourier.circuit_spectrum, and other usage details, please see the fourier.qnode_spectrum docstring.

• Two new methods were added to the Device API, allowing PennyLane devices increased control over circuit decompositions. (#1651)

• Device.expand_fn(tape) -> tape: expands a tape such that it is supported by the device. By default, performs the standard device-specific gate set decomposition done in the default QNode. Devices may overwrite this method in order to define their own decomposition logic.

Note that the numerical result after applying this method should remain unchanged; PennyLane will assume that the expanded tape returns exactly the same value as the original tape when executed.

• Device.batch_transform(tape) -> (tapes, processing_fn): preprocesses the tape in the case where the device needs to generate multiple circuits to execute from the input circuit. The requirement of a post-processing function makes this distinct to the expand_fn method above.

By default, this method applies the transform

$\left\langle \sum_i c_i h_i\right\rangle → \sum_i c_i \left\langle h_i \right\rangle$

if expval(H) is present on devices that do not natively support Hamiltonians with non-commuting terms.

• A new class has been added to store operator attributes, such as self_inverses, and composable_rotation, as a list of operation names. (#1763)

A number of such attributes, for the purpose of compilation transforms, can be found in ops/qubit/attributes.py, but the class can also be used to create your own. For example, we can create a new Attribute, pauli_ops, like so:

>>> from pennylane.ops.qubit.attributes import Attribute
>>> pauli_ops = Attribute(["PauliX", "PauliY", "PauliZ"])


We can check either a string or an Operation for inclusion in this set:

>>> qml.PauliX(0) in pauli_ops
True
False


We can also dynamically add operators to the sets at runtime. This is useful for adding custom operations to the attributes such as composable_rotations and self_inverses that are used in compilation transforms. For example, suppose you have created a new Operation, MyGate, which you know to be its own inverse. Adding it to the set, like so

>>> from pennylane.ops.qubit.attributes import self_inverses


will enable the gate to be considered by the cancel_inverses compilation transform if two such gates are adjacent in a circuit.

### Improvements

• The qml.metric_tensor transform has been improved with regards to both function and performance. (#1638) (#1721)

• If the underlying device supports batch execution of circuits, the quantum circuits required to compute the metric tensor elements will be automatically submitted as a batched job. This can lead to significant performance improvements for devices with a non-trivial job submission overhead.

• Previously, the transform would only return the metric tensor with respect to gate arguments, and ignore any classical processing inside the QNode, even very trivial classical processing such as parameter permutation. The metric tensor now takes into account classical processing, and returns the metric tensor with respect to QNode arguments, not simply gate arguments:

>>> @qml.qnode(dev)
... def circuit(x):
...     qml.RX(x[0], wires=0)
...     qml.CNOT(wires=[0, 1])
...     qml.RY(x[1] ** 2, wires=1)
...     qml.RY(x[1], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> x = np.array([0.1, 0.2], requires_grad=True)
>>> qml.metric_tensor(circuit)(x)
array([[0.25      , 0.        ],
[0.        , 0.28750832]])


To revert to the previous behaviour of returning the metric tensor with respect to gate arguments, qml.metric_tensor(qnode, hybrid=False) can be passed.

>>> qml.metric_tensor(circuit, hybrid=False)(x)
array([[0.25      , 0.        , 0.        ],
[0.        , 0.25      , 0.        ],
[0.        , 0.        , 0.24750832]])

• The metric tensor transform now works with a larger set of operations. In particular, all operations that have a single variational parameter and define a generator are now supported. In addition to a reduction in decomposition overhead, the change also results in fewer circuit evaluations.

• The expansion rule in the qml.metric_tensor transform has been changed. (#1721)

If hybrid=False, the changed expansion rule might lead to a changed output.

• The ApproxTimeEvolution template can now be used with Hamiltonians that have trainable coefficients. (#1789)

Resulting QNodes can be differentiated with respect to both the time parameter and the Hamiltonian coefficients.

dev = qml.device('default.qubit', wires=2)
obs = [qml.PauliX(0) @ qml.PauliY(1), qml.PauliY(0) @ qml.PauliX(1)]

@qml.qnode(dev)
def circuit(coeffs, t):
H = qml.Hamiltonian(coeffs, obs)
qml.templates.ApproxTimeEvolution(H, t, 2)
return qml.expval(qml.PauliZ(0))

>>> t = np.array(0.54, requires_grad=True)
>>> coeffs = np.array([-0.6, 2.0], requires_grad=True)
(array([-1.07813375, -1.07813375]), array(-2.79516158))


All differentiation methods, including backpropagation and the parameter-shift rule, are supported.

• Quantum function transforms and batch transforms can now be applied to devices. Once applied to a device, any quantum function executed on the modified device will be transformed prior to execution. (#1809) (#1810)

dev = qml.device("default.mixed", wires=1)
dev = qml.transforms.merge_rotations()(dev)

@qml.beta.qnode(dev)
def f(w, x, y, z):
qml.RX(w, wires=0)
qml.RX(x, wires=0)
qml.RX(y, wires=0)
qml.RX(z, wires=0)
return qml.expval(qml.PauliZ(0))

>>> print(f(0.9, 0.4, 0.5, 0.6))
-0.7373937155412453
>>> print(qml.draw(f, expansion_strategy="device")(0.9, 0.4, 0.5, 0.6))
0: ──RX(2.4)──┤ ⟨Z⟩

• It is now possible to draw QNodes that have been transformed by a ‘batch transform’; that is, a transform that maps a single QNode into multiple circuits under the hood. Examples of batch transforms include @qml.metric_tensor and @qml.gradients. (#1762)

For example, consider the parameter-shift rule, which generates two circuits per parameter; one circuit that has the parameter shifted forward, and another that has the parameter shifted backwards:

dev = qml.device("default.qubit", wires=2)

@qml.beta.qnode(dev)
def circuit(x):
qml.RX(x, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(wires=0))

>>> print(qml.draw(circuit)(0.6))
0: ──RX(2.17)──╭C──┤ ⟨Z⟩
1: ────────────╰X──┤

0: ──RX(-0.971)──╭C──┤ ⟨Z⟩
1: ──────────────╰X──┤

• Support for differentiable execution of batches of circuits has been extended to the JAX interface for scalar functions, via the beta pennylane.interfaces.batch module. (#1634) (#1685)

For example using the execute function from the pennylane.interfaces.batch module:

from pennylane.interfaces.batch import execute

def cost_fn(x):
with qml.tape.JacobianTape() as tape1:
qml.RX(x[0], wires=[0])
qml.RY(x[1], wires=[1])
qml.CNOT(wires=[0, 1])
qml.var(qml.PauliZ(0) @ qml.PauliX(1))

with qml.tape.JacobianTape() as tape2:
qml.RX(x[0], wires=0)
qml.RY(x[0], wires=1)
qml.CNOT(wires=[0, 1])
qml.probs(wires=1)

result = execute(
[tape1, tape2], dev,
)
return (result[0] + result[1][0, 0])[0]


• All qubit operations have been re-written to use the qml.math framework for internal classical processing and the generation of their matrix representations. As a result these representations are now fully differentiable, and the framework-specific device classes no longer need to maintain framework-specific versions of these matrices. (#1749) (#1802)

• The use of expval(H), where H is a cost Hamiltonian generated by the qaoa module, has been sped up. This was achieved by making PennyLane decompose a circuit with an expval(H) measurement into subcircuits if the Hamiltonian.grouping_indices attribute is set, and setting this attribute in the relevant qaoa module functions. (#1718)

• Operations can now have gradient recipes that depend on the state of the operation. (#1674)

For example, this allows for gradient recipes that are parameter dependent:

class RX(qml.RX):

@property
# The gradient is given by [f(2x) - f(0)] / (2 sin(x)), by subsituting
# shift = x into the two term parameter-shift rule.
x = self.data[0]
c = 0.5 / np.sin(x)
return ([[c, 0.0, 2 * x], [-c, 0.0, 0.0]],)

• Shots can now be passed as a runtime argument to transforms that execute circuits in batches, similarly to QNodes. (#1707)

An example of such a transform are the gradient transforms in the qml.gradients module. As a result, we can now call gradient transforms (such as qml.gradients.param_shift) and set the number of shots at runtime.

>>> dev = qml.device("default.qubit", wires=1, shots=1000)
>>> @qml.beta.qnode(dev)
... def circuit(x):
...     qml.RX(x, wires=0)
...     return qml.expval(qml.PauliZ(0))
array([[-1., -1., -1., -1., -1.,  0., -1.,  0., -1.,  0.]])
array([[-0.12298782]])

• Templates are now top level imported and can be used directly e.g. qml.QFT(wires=0). (#1779)

• qml.probs now accepts an attribute op that allows to rotate the computational basis and get the probabilities in the rotated basis. (#1692)

• Refactored the expand_fn functionality in the Device class to avoid any edge cases leading to failures with plugins. (#1838)

• Updated the qml.QNGOptimizer.step_and_cost method to avoid the use of deprecated functionality. (#1834)

• Added a custom torch.to_numpy implementation to pennylane/math/single_dispatch.py to ensure compabilitity with PyTorch 1.10. (#1824) (#1825)

• The default for an Operation‘s control_wires attribute is now an empty Wires object instead of the attribute raising a NonImplementedError. (#1821)

• qml.circuit_drawer.MPLDrawer will now automatically rotate and resize text to fit inside the rectangle created by the box_gate method. (#1764)

• Operators now have a label method to determine how they are drawn. This will eventually override the RepresentationResolver class. (#1678)

• The operation label method now supports string variables. (#1815)

• A new utility class qml.BooleanFn is introduced. It wraps a function that takes a single argument and returns a Boolean. (#1734)

After wrapping, qml.BooleanFn can be called like the wrapped function, and multiple instances can be manipulated and combined with the bitwise operators &, | and ~.

• There is a new utility function qml.math.is_independent that checks whether a callable is independent of its arguments. (#1700)

This function is experimental and might behave differently than expected.

Note that the test relies on both numerical and analytical checks, except when using the PyTorch interface which only performs a numerical check. It is known that there are edge cases on which this test will yield wrong results, in particular non-smooth functions may be problematic. For details, please refer to the is_indpendent docstring.

• The qml.beta.QNode now supports the qml.qnn module. (#1748)

• @qml.beta.QNode now supports the qml.specs transform. (#1739)

• qml.circuit_drawer.drawable_layers and qml.circuit_drawer.drawable_grid process a list of operations to layer positions for drawing. (#1639)

• qml.transforms.batch_transform now accepts expand_fns that take additional arguments and keyword arguments. In fact, expand_fn and transform_fn now must have the same signature. (#1721)

• The qml.batch_transform decorator is now ignored during Sphinx builds, allowing the correct signature to display in the built documentation. (#1733)

• The tests for qubit operations are split into multiple files. (#1661)

• The transform for the Jacobian of the classical preprocessing within a QNode, qml.transforms.classical_jacobian, now takes a keyword argument argnum to specify the QNode argument indices with respect to which the Jacobian is computed. (#1645)

An example for the usage of argnum is

@qml.qnode(dev)
def circuit(x, y, z):
qml.RX(qml.math.sin(x), wires=0)
qml.CNOT(wires=[0, 1])
qml.RY(y ** 2, wires=1)
qml.RZ(1 / z, wires=1)
return qml.expval(qml.PauliZ(0))

jac_fn = qml.transforms.classical_jacobian(circuit, argnum=[1, 2])


The Jacobian can then be computed at specified parameters.

>>> x, y, z = np.array([0.1, -2.5, 0.71])
>>> jac_fn(x, y, z)
(array([-0., -5., -0.]), array([-0.        , -0.        , -1.98373339]))


The returned arrays are the derivatives of the three parametrized gates in the circuit with respect to y and z respectively.

There also are explicit tests for classical_jacobian now, which previously was tested implicitly via its use in the metric_tensor transform.

For more usage details, please see the classical Jacobian docstring.

• A new utility function qml.math.is_abstract(tensor) has been added. This function returns True if the tensor is abstract; that is, it has no value or shape. This can occur if within a function that has been just-in-time compiled. (#1845)

• qml.circuit_drawer.CircuitDrawer can accept a string for the charset keyword, instead of a CharSet object. (#1640)

• qml.math.sort will now return only the sorted torch tensor and not the corresponding indices, making sort consistent across interfaces. (#1691)

• Specific QNode execution options are now re-used by batch transforms to execute transformed QNodes. (#1708)

• To standardize across all optimizers, qml.optimize.AdamOptimizer now also uses accumulation (in form of collections.namedtuple) to keep track of running quantities. Before it used three variables fm, sm and t. (#1757)

### Breaking changes

• The operator attributes has_unitary_generator, is_composable_rotation, is_self_inverse, is_symmetric_over_all_wires, and is_symmetric_over_control_wires have been removed as attributes from the base class. They have been replaced by the sets that store the names of operations with similar properties in ops/qubit/attributes.py. (#1763)

• The qml.inv function has been removed, qml.adjoint should be used instead. (#1778)

• The input signature of an expand_fn used in a batch_transform now must have the same signature as the provided transform_fn, and vice versa. (#1721)

• The default.qubit.torch device automatically determines if computations should be run on a CPU or a GPU and doesn’t take a torch_device argument anymore. (#1705)

• The utility function qml.math.requires_grad now returns True when using Autograd if and only if the requires_grad=True attribute is set on the NumPy array. Previously, this function would return True for all NumPy arrays and Python floats, unless requires_grad=False was explicitly set. (#1638)

• The operation qml.Interferometer has been renamed qml.InterferometerUnitary in order to distinguish it from the template qml.templates.Interferometer. (#1714)

• The qml.transforms.invisible decorator has been replaced with qml.tape.stop_recording, which may act as a context manager as well as a decorator to ensure that contained logic is non-recordable or non-queueable within a QNode or quantum tape context. (#1754)

• Templates SingleExcitationUnitary and DoubleExcitationUnitary have been renamed to FermionicSingleExcitation and FermionicDoubleExcitation, respectively. (#1822)

### Deprecations

• Allowing cost functions to be differentiated using qml.grad or qml.jacobian without explicitly marking parameters as trainable is being deprecated, and will be removed in an upcoming release. Please specify the requires_grad attribute for every argument, or specify argnum when using qml.grad or qml.jacobian. (#1773)

The following raises a warning in v0.19.0 and will raise an error in an upcoming release:

import pennylane as qml

dev = qml.device('default.qubit', wires=1)

@qml.qnode(dev)
def test(x):
qml.RY(x, wires=[0])
return qml.expval(qml.PauliZ(0))

par = 0.3


Preferred approaches include specifying the requires_grad attribute:

import pennylane as qml
from pennylane import numpy as np

dev = qml.device('default.qubit', wires=1)

@qml.qnode(dev)
def test(x):
qml.RY(x, wires=[0])
return qml.expval(qml.PauliZ(0))



Or specifying the argnum argument when using qml.grad or qml.jacobian:

import pennylane as qml

dev = qml.device('default.qubit', wires=1)

@qml.qnode(dev)
def test(x):
qml.RY(x, wires=[0])
return qml.expval(qml.PauliZ(0))

par = 0.3


• The default.tensor device from the beta folder is no longer maintained and has been deprecated. It will be removed in future releases. (#1851)

• The qml.metric_tensor and qml.QNGOptimizer keyword argument diag_approx is deprecated. Approximations can be controlled with the more fine-grained approx keyword argument, with approx="block-diag" (the default) reproducing the old behaviour. (#1721) (#1834)

• The template decorator is now deprecated with a warning message and will be removed in release v0.20.0. It has been removed from different PennyLane functions. (#1794) (#1808)

• The qml.fourier.spectrum function has been renamed to qml.fourier.circuit_spectrum, in order to clearly separate the new qnode_spectrum function from this one. qml.fourier.spectrum is now an alias for circuit_spectrum but is flagged for deprecation and will be removed soon. (#1681)

• The init module, which contains functions to generate random parameter tensors for templates, is flagged for deprecation and will be removed in the next release cycle. Instead, the templates’ shape method can be used to get the desired shape of the tensor, which can then be generated manually. (#1689)

To generate the parameter tensors, the np.random.normal and np.random.uniform functions can be used (just like in the init module). Considering the default arguments of these functions as of NumPy v1.21, some non-default options were used by the init module:

• All functions generating normally distributed parameters used np.random.normal by passing scale=0.1;

• Most functions generating uniformly distributed parameters (except for certain CVQNN initializers) used np.random.uniform by passing high=2*math.pi;

• The cvqnn_layers_r_uniform, cvqnn_layers_a_uniform, cvqnn_layers_kappa_uniform functions used np.random.uniform by passing high=0.1.

• The QNode.draw method has been deprecated, and will be removed in an upcoming release. Please use the qml.draw transform instead. (#1746)

• The QNode.metric_tensor method has been deprecated, and will be removed in an upcoming release. Please use the qml.metric_tensor transform instead. (#1638)

• The pad parameter of the qml.AmplitudeEmbedding template has been removed. It has instead been renamed to the pad_with parameter. (#1805)

### Bug fixes

• Fixes a bug where qml.math.dot failed to work with @tf.function autograph mode. (#1842)

• Fixes a bug where in rare instances the parameters of a tape are returned unsorted by Tape.get_parameters. (#1836)

• Fixes a bug with the arrow width in the measure of qml.circuit_drawer.MPLDrawer. (#1823)

• The helper functions qml.math.block_diag and qml.math.scatter_element_add now are entirely differentiable when using Autograd. Previously only indexed entries of the block diagonal could be differentiated, while the derivative w.r.t to the second argument of qml.math.scatter_element_add dispatched to NumPy instead of Autograd. (#1816) (#1818)

• Fixes a bug such that the original shot vector information of a device is preserved, so that outside the context manager the device remains unchanged. (#1792)

• Modifies qml.math.take to be compatible with a breaking change released in JAX 0.2.24 and ensure that PennyLane supports this JAX version. (#1769)

• Fixes a bug where the GPU cannot be used with qml.qnn.TorchLayer. (#1705)

• Fix a bug where the devices cache the same result for different observables return types. (#1719)

• Fixed a bug of the default circuit drawer where having more measurements compared to the number of measurements on any wire raised a KeyError. (#1702)

• Fix a bug where it was not possible to use jax.jit on a QNode when using QubitStateVector. (#1683)

• The device suite tests can now execute successfully if no shots configuration variable is given. (#1641)

• Fixes a bug where the qml.gradients.param_shift transform would raise an error while attempting to compute the variance of a QNode with ragged output. (#1646)

• Fixes a bug in default.mixed, to ensure that returned probabilities are always non-negative. (#1680)

• Fixes a bug where gradient transforms would fail to apply to QNodes containing classical processing. (#1699)

• Fixes a bug where the the parameter-shift method was not correctly using the fallback gradient function when all circuit parameters required the fallback. (#1782)

### Documentation

• Corrects the docstring of ExpvalCost by adding wires to the signature of the ansatz argument. (#1715)

• Updated docstring examples using the qchem.molecular_hamiltonian function. (#1724)

• All instances of qnode.draw() have been updated to instead use the transform qml.draw(qnode). (#1750)

• Add the jax interface in QNode Documentation. (#1755)

• Reorganized all the templates related to quantum chemistry under a common header Quantum Chemistry templates. (#1822)

### Contributors

This release contains contributions from (in alphabetical order):

Catalina Albornoz, Juan Miguel Arrazola, Utkarsh Azad, Akash Narayanan B, Sam Banning, Thomas Bromley, Jack Ceroni, Alain Delgado, Olivia Di Matteo, Andrew Gardhouse, Anthony Hayes, Theodor Isacsson, David Ittah, Josh Izaac, Soran Jahangiri, Nathan Killoran, Christina Lee, Guillermo Alonso-Linaje, Romain Moyard, Lee James O’Riordan, Carrie-Anne Rubidge, Maria Schuld, Rishabh Singh, Jay Soni, Ingrid Strandberg, Antal Száva, Teresa Tamayo-Mendoza, Rodrigo Vargas, Cody Wang, David Wierichs, Moritz Willmann.

orphan