# Source code for pennylane.ops.qubit.parametric_ops_multi_qubit

# Copyright 2018-2023 Xanadu Quantum Technologies Inc.

# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# pylint: disable=too-many-arguments
"""
This submodule contains the discrete-variable quantum operations that are the
core parameterized gates.
"""
# pylint:disable=abstract-method,arguments-differ,protected-access,invalid-overridden-method
import functools
from operator import matmul
import numpy as np

import pennylane as qml
from pennylane.math import expand_matrix
from pennylane.operation import AnyWires, Operation
from pennylane.utils import pauli_eigs
from pennylane.wires import Wires

from .non_parametric_ops import Hadamard, PauliX, PauliY, PauliZ
from .parametric_ops_single_qubit import _can_replace, stack_last, RX, RY, RZ, PhaseShift

[docs]class MultiRZ(Operation):
r"""
Arbitrary multi Z rotation.

.. math::

MultiRZ(\theta) = \exp(-i \frac{\theta}{2} Z^{\otimes n})

**Details:**

* Number of wires: Any
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: :math:\frac{d}{d\theta}f(MultiRZ(\theta)) = \frac{1}{2}\left[f(MultiRZ(\theta +\pi/2)) - f(MultiRZ(\theta-\pi/2))\right]
where :math:f is an expectation value depending on :math:MultiRZ(\theta).

.. note::

If the MultiRZ gate is not supported on the targeted device, PennyLane
will decompose the gate using :class:~.RZ and :class:~.CNOT gates.

Args:
theta (tensor_like or float): rotation angle :math:\theta
wires (Sequence[int] or int): the wires the operation acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = AnyWires
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

parameter_frequencies = [(1,)]

def __init__(self, theta, wires=None, do_queue=True, id=None):
wires = Wires(wires)
self.hyperparameters["num_wires"] = len(wires)
super().__init__(theta, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_matrix(theta, num_wires):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.MultiRZ.matrix

Args:
theta (tensor_like or float): rotation angle
num_wires (int): number of wires the rotation acts on

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.MultiRZ.compute_matrix(torch.tensor(0.1), 2)
tensor([[0.9988-0.0500j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.9988+0.0500j, 0.0000+0.0000j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000+0.0000j, 0.9988+0.0500j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9988-0.0500j]])
"""
eigs = qml.math.convert_like(pauli_eigs(num_wires), theta)

if qml.math.get_interface(theta) == "tensorflow":
theta = qml.math.cast_like(theta, 1j)
eigs = qml.math.cast_like(eigs, 1j)

if qml.math.ndim(theta) == 0:
return qml.math.diag(qml.math.exp(-0.5j * theta * eigs))

diags = qml.math.exp(qml.math.outer(-0.5j * theta, eigs))
return diags[:, :, np.newaxis] * qml.math.cast_like(
qml.math.eye(2**num_wires, like=diags), diags
)

[docs]    def generator(self):
return -0.5 * functools.reduce(matmul, [PauliZ(w) for w in self.wires])

[docs]    @staticmethod
def compute_eigvals(theta, num_wires):  # pylint: disable=arguments-differ
r"""Eigenvalues of the operator in the computational basis (static method).

If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger},
the operator can be reconstructed as

.. math:: O = U \Sigma U^{\dagger},

where :math:\Sigma is the diagonal matrix containing the eigenvalues.

Otherwise, no particular order for the eigenvalues is guaranteed.

.. seealso:: :meth:~.MultiRZ.eigvals

Args:
theta (tensor_like or float): rotation angle
num_wires (int): number of wires the rotation acts on

Returns:
tensor_like: eigenvalues

**Example**

>>> qml.MultiRZ.compute_eigvals(torch.tensor(0.5), 3)
tensor([0.9689-0.2474j, 0.9689+0.2474j, 0.9689+0.2474j, 0.9689-0.2474j,
0.9689+0.2474j, 0.9689-0.2474j, 0.9689-0.2474j, 0.9689+0.2474j])
"""
eigs = qml.math.convert_like(pauli_eigs(num_wires), theta)

if qml.math.get_interface(theta) == "tensorflow":
theta = qml.math.cast_like(theta, 1j)
eigs = qml.math.cast_like(eigs, 1j)

if qml.math.ndim(theta) == 0:
return qml.math.exp(-0.5j * theta * eigs)

return qml.math.exp(qml.math.outer(-0.5j * theta, eigs))

[docs]    @staticmethod
def compute_decomposition(
theta, wires, **kwargs
):  # pylint: disable=arguments-differ,unused-argument
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.MultiRZ.decomposition.

Args:
theta (float): rotation angle :math:\theta
wires (Iterable, Wires): the wires the operation acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.MultiRZ.compute_decomposition(1.2, wires=(0,1))
[CNOT(wires=[1, 0]), RZ(1.2, wires=[0]), CNOT(wires=[1, 0])]

"""
ops = [qml.CNOT(wires=(w0, w1)) for w0, w1 in zip(wires[~0:0:-1], wires[~1::-1])]
ops.append(RZ(theta, wires=wires[0]))
ops += [qml.CNOT(wires=(w0, w1)) for w0, w1 in zip(wires[1:], wires[:~0])]

return ops

return MultiRZ(-self.parameters[0], wires=self.wires)

[docs]    def pow(self, z):
return [MultiRZ(self.data[0] * z, wires=self.wires)]

[docs]    def simplify(self):
theta = self.data[0] % (4 * np.pi)

if _can_replace(theta, 0):
return qml.Identity(wires=self.wires[0])

return MultiRZ(theta, wires=self.wires)

[docs]class PauliRot(Operation):
r"""
Arbitrary Pauli word rotation.

.. math::

RP(\theta, P) = \exp(-i \frac{\theta}{2} P)

**Details:**

* Number of wires: Any
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: :math:\frac{d}{d\theta}f(RP(\theta)) = \frac{1}{2}\left[f(RP(\theta +\pi/2)) - f(RP(\theta-\pi/2))\right]
where :math:f is an expectation value depending on :math:RP(\theta).

.. note::

If the PauliRot gate is not supported on the targeted device, PennyLane
will decompose the gate using :class:~.RX, :class:~.Hadamard, :class:~.RZ
and :class:~.CNOT gates.

Args:
theta (float): rotation angle :math:\theta
pauli_word (string): the Pauli word defining the rotation
wires (Sequence[int] or int): the wire the operation acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)

**Example**

>>> dev = qml.device('default.qubit', wires=1)
>>> @qml.qnode(dev)
... def example_circuit():
...     qml.PauliRot(0.5, 'X',  wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> print(example_circuit())
0.8775825618903724
"""
num_wires = AnyWires
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

do_check_domain = False
parameter_frequencies = [(1,)]

_ALLOWED_CHARACTERS = "IXYZ"

_PAULI_CONJUGATION_MATRICES = {
"Y": RX.compute_matrix(np.pi / 2),
"Z": np.array([[1, 0], [0, 1]]),
}

def __init__(self, theta, pauli_word, wires=None, do_queue=True, id=None):
super().__init__(theta, wires=wires, do_queue=do_queue, id=id)
self.hyperparameters["pauli_word"] = pauli_word

if not PauliRot._check_pauli_word(pauli_word):
raise ValueError(
f'The given Pauli word "{pauli_word}" contains characters that are not allowed. '
"Allowed characters are I, X, Y and Z"
)

num_wires = 1 if isinstance(wires, int) else len(wires)

if not len(pauli_word) == num_wires:
raise ValueError(
f"The given Pauli word has length {len(pauli_word)}, length "
f"{num_wires} was expected for wires {wires}"
)

def __repr__(self):
return f"PauliRot({self.data[0]}, {self.hyperparameters['pauli_word']}, wires={self.wires.tolist()})"

[docs]    def label(self, decimals=None, base_label=None, cache=None):
r"""A customizable string representation of the operator.

Args:
decimals=None (int): If None, no parameters are included. Else,
specifies how to round the parameters.
base_label=None (str): overwrite the non-parameter component of the label
cache=None (dict): dictionary that caries information between label calls
in the same drawing

Returns:
str: label to use in drawings

**Example:**

>>> op = qml.PauliRot(0.1, "XYY", wires=(0,1,2))
>>> op.label()
'RXYY'
>>> op.label(decimals=2)
'RXYY\n(0.10)'
>>> op.label(base_label="PauliRot")
'PauliRot\n(0.10)'

"""
pauli_word = self.hyperparameters["pauli_word"]
op_label = base_label or ("R" + pauli_word)

# TODO[dwierichs]: Implement a proper label for parameter-broadcasted operators
if decimals is not None and self.batch_size is None:
param_string = f"\n({qml.math.asarray(self.parameters[0]):.{decimals}f})"
op_label += param_string

return op_label

@staticmethod
def _check_pauli_word(pauli_word):
"""Check that the given Pauli word has correct structure.

Args:
pauli_word (str): Pauli word to be checked

Returns:
bool: Whether the Pauli word has correct structure.
"""
return all(pauli in PauliRot._ALLOWED_CHARACTERS for pauli in set(pauli_word))

[docs]    @staticmethod
def compute_matrix(theta, pauli_word):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.PauliRot.matrix

Args:
theta (tensor_like or float): rotation angle
pauli_word (str): string representation of Pauli word

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.PauliRot.compute_matrix(0.5, 'X')
[[9.6891e-01+4.9796e-18j 2.7357e-17-2.4740e-01j]
[2.7357e-17-2.4740e-01j 9.6891e-01+4.9796e-18j]]
"""
if not PauliRot._check_pauli_word(pauli_word):
raise ValueError(
f'The given Pauli word "{pauli_word}" contains characters that are not allowed. '
"Allowed characters are I, X, Y and Z"
)

interface = qml.math.get_interface(theta)

if interface == "tensorflow":
theta = qml.math.cast_like(theta, 1j)

# Simplest case is if the Pauli is the identity matrix
if set(pauli_word) == {"I"}:
exp = qml.math.exp(-0.5j * theta)
iden = qml.math.eye(2 ** len(pauli_word), like=theta)
if qml.math.get_interface(theta) == "tensorflow":
iden = qml.math.cast_like(iden, 1j)
if qml.math.get_interface(theta) == "torch":
td = exp.device
iden = iden.to(td)

if qml.math.ndim(theta) == 0:
return exp * iden

return qml.math.stack([e * iden for e in exp])

# We first generate the matrix excluding the identity parts and expand it afterwards.
# To this end, we have to store on which wires the non-identity parts act
non_identity_wires, non_identity_gates = zip(
*[(wire, gate) for wire, gate in enumerate(pauli_word) if gate != "I"]
)

multi_Z_rot_matrix = MultiRZ.compute_matrix(theta, len(non_identity_gates))

# now we conjugate with Hadamard and RX to create the Pauli string
conjugation_matrix = functools.reduce(
qml.math.kron,
[PauliRot._PAULI_CONJUGATION_MATRICES[gate] for gate in non_identity_gates],
)
if interface == "tensorflow":
conjugation_matrix = qml.math.cast_like(conjugation_matrix, 1j)
# Note: we use einsum with reverse arguments here because it is not multi-dispatched
# and the tensordot containing multi_Z_rot_matrix should decide about the interface
return expand_matrix(
qml.math.einsum(
"...jk,ij->...ik",
qml.math.tensordot(multi_Z_rot_matrix, conjugation_matrix, axes=[[-1], [0]]),
qml.math.conj(conjugation_matrix),
),
non_identity_wires,
list(range(len(pauli_word))),
)

[docs]    def generator(self):
pauli_word = self.hyperparameters["pauli_word"]
wire_map = {w: i for i, w in enumerate(self.wires)}
return -0.5 * qml.pauli.string_to_pauli_word(pauli_word, wire_map=wire_map)

[docs]    @staticmethod
def compute_eigvals(theta, pauli_word):  # pylint: disable=arguments-differ
r"""Eigenvalues of the operator in the computational basis (static method).

If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger},
the operator can be reconstructed as

.. math:: O = U \Sigma U^{\dagger},

where :math:\Sigma is the diagonal matrix containing the eigenvalues.

Otherwise, no particular order for the eigenvalues is guaranteed.

.. seealso:: :meth:~.PauliRot.eigvals

Returns:
tensor_like: eigenvalues

**Example**

>>> qml.PauliRot.compute_eigvals(torch.tensor(0.5), "X")
tensor([0.9689-0.2474j, 0.9689+0.2474j])
"""
if qml.math.get_interface(theta) == "tensorflow":
theta = qml.math.cast_like(theta, 1j)

# Identity must be treated specially because its eigenvalues are all the same
if set(pauli_word) == {"I"}:
exp = qml.math.exp(-0.5j * theta)
ones = qml.math.ones(2 ** len(pauli_word), like=theta)
if qml.math.get_interface(theta) == "tensorflow":
ones = qml.math.cast_like(ones, 1j)

if qml.math.ndim(theta) == 0:
return exp * ones

return qml.math.tensordot(exp, ones, axes=0)

return MultiRZ.compute_eigvals(theta, len(pauli_word))

[docs]    @staticmethod
def compute_decomposition(theta, wires, pauli_word):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.PauliRot.decomposition.

Args:
theta (float): rotation angle :math:\theta
wires (Iterable, Wires): the wires the operation acts on
pauli_word (string): the Pauli word defining the rotation

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.PauliRot.compute_decomposition(1.2, "XY", wires=(0,1))
RX(1.5707963267948966, wires=[1]),
MultiRZ(1.2, wires=[0, 1]),
RX(-1.5707963267948966, wires=[1])]

"""
if isinstance(wires, int):  # Catch cases when the wire is passed as a single int.
wires = [wires]

# Check for identity and do nothing
if set(pauli_word) == {"I"}:
return []

active_wires, active_gates = zip(
*[(wire, gate) for wire, gate in zip(wires, pauli_word) if gate != "I"]
)

ops = []
for wire, gate in zip(active_wires, active_gates):
if gate == "X":
elif gate == "Y":
ops.append(RX(np.pi / 2, wires=[wire]))

ops.append(MultiRZ(theta, wires=list(active_wires)))

for wire, gate in zip(active_wires, active_gates):
if gate == "X":
elif gate == "Y":
ops.append(RX(-np.pi / 2, wires=[wire]))
return ops

return PauliRot(-self.parameters[0], self.hyperparameters["pauli_word"], wires=self.wires)

[docs]    def pow(self, z):
return [PauliRot(self.data[0] * z, self.hyperparameters["pauli_word"], wires=self.wires)]

[docs]class PCPhase(Operation):
r"""PCPhase(phi, dim, wires)
A projector-controlled phase gate.

This gate applies a complex phase :math:e^{i\phi} to the first :math:dim
basis vectors of the input state while applying a complex phase :math:e^{-i \phi}
to the remaining basis vectors. For example, consider the 2-qubit case where :math:dim = 3:

.. math:: \Pi(\phi) = \begin{bmatrix}
e^{i\phi} & 0 & 0 & 0 \\
0 & e^{i\phi} & 0 & 0 \\
0 & 0 & e^{i\phi} & 0 \\
0 & 0 & 0 & e^{-i\phi}
\end{bmatrix}.

**Details:**

* Number of wires: Any (the operation can act on any number of wires)
* Number of parameters: 1
* Number of dimensions per parameter: (0,)

Args:
phi (float): rotation angle :math:\phi
dim (int): the dimension of the subspace
wires (Iterable[int, str], Wires): the wires the operation acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)

**Example:**

We can define a circuit using :class:~.PCPhase as follows:

>>> dev = qml.device('default.qubit', wires=2)
>>> @qml.qnode(dev)
>>> def example_circuit():
...     qml.PCPhase(0.27, dim = 2, wires=range(2))
...     return qml.state()

The resulting operation applies a complex phase :math:e^{0.27i} to the first :math:dim = 2
basis vectors and :math:e^{-0.27i} to the remaining basis vectors.

>>> print(np.round(qml.matrix(example_circuit)(),2))
[[0.96+0.27j 0.  +0.j   0.  +0.j   0.  +0.j  ]
[0.  +0.j   0.96+0.27j 0.  +0.j   0.  +0.j  ]
[0.  +0.j   0.  +0.j   0.96-0.27j 0.  +0.j  ]
[0.  +0.j   0.  +0.j   0.  +0.j   0.96-0.27j]]

We can also choose a different :math:dim value to apply the phase shift to a different set of
basis vectors as follows:

>>> pc_op = qml.PCPhase(1.23, dim=3, wires=[1, 2])
>>> print(np.round(qml.matrix(pc_op),2))
[[0.33+0.94j 0.  +0.j   0.  +0.j   0.  +0.j  ]
[0.  +0.j   0.33+0.94j 0.  +0.j   0.  +0.j  ]
[0.  +0.j   0.  +0.j   0.33+0.94j 0.  +0.j  ]
[0.  +0.j   0.  +0.j   0.  +0.j   0.33-0.94j]]
"""
num_wires = AnyWires
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""
ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

basis = "Z"
parameter_frequencies = [(2,)]

[docs]    def generator(self):
dim, shape = self.hyperparameters["dimension"]
mat = np.diag([1 if index < dim else -1 for index in range(shape)])
return qml.Hermitian(mat, wires=self.wires)

def __init__(self, phi, dim, wires, do_queue=True, id=None):
wires = wires if isinstance(wires, Wires) else Wires(wires)

if not (isinstance(dim, int) and (dim <= 2 ** len(wires))):
raise ValueError(
f"The projected dimension {dim} must be an integer that is less than or equal to "
f"the max size of the matrix {2 ** len(wires)}. Try adding more wires."
)

super().__init__(phi, wires=wires, do_queue=do_queue, id=id)
self.hyperparameters["dimension"] = (dim, 2 ** len(wires))

[docs]    @staticmethod
def compute_matrix(*params, **hyperparams):
"""Get the matrix representation of Pi-controlled phase unitary."""
phi = params[0]
d, t = hyperparams["dimension"]

if qml.math.get_interface(phi) == "tensorflow":
p = qml.math.exp(1j * qml.math.cast_like(phi, 1j))
minus_p = qml.math.exp(-1j * qml.math.cast_like(phi, 1j))
zeros = qml.math.zeros_like(p)

columns = []
for i in range(t):
columns.append(
[p if j == i else zeros for j in range(t)]
if i < d
else [minus_p if j == i else zeros for j in range(t)]
)
r = qml.math.stack(columns, like="tensorflow", axis=-2)
return r

arg = 1j * phi
prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi)

if qml.math.ndim(arg) == 0:
return qml.math.diag(qml.math.exp(arg * prefactors))

diags = qml.math.exp(qml.math.outer(arg, prefactors))
return qml.math.stack(qml.math.diag(d) for d in diags)

[docs]    @staticmethod
def compute_eigvals(*params, **hyperparams):
"""Get the eigvals for the Pi-controlled phase unitary."""
phi = params[0]
d, t = hyperparams["dimension"]

if qml.math.get_interface(phi) == "tensorflow":
phase = qml.math.exp(1j * qml.math.cast_like(phi, 1j))
minus_phase = qml.math.exp(-1j * qml.math.cast_like(phi, 1j))
return stack_last([phase if index < d else minus_phase for index in range(t)])

arg = 1j * phi
prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi)

if qml.math.ndim(phi) == 0:
product = arg * prefactors
else:
product = qml.math.outer(arg, prefactors)
return qml.math.exp(product)

[docs]    @staticmethod
def compute_decomposition(*params, wires=None, **hyperparams):
r"""Representation of the operator as a product of other operators (static method).

.. math:: O = O_1 O_2 \dots O_n.

.. note::

Operations making up the decomposition should be queued within the
compute_decomposition method.

.. seealso:: :meth:~.Operator.decomposition.

Args:
params (list): trainable parameters of the operator, as stored in the parameters attribute
wires (Iterable[Any], Wires): wires that the operator acts on
hyperparams (dict): non-trainable hyper-parameters of the operator, as stored in the hyperparameters attribute

Returns:
list[Operator]: decomposition of the operator
"""
phi = params[0]
k, n = hyperparams["dimension"]

def _get_op_from_binary_rep(binary_rep, theta, wires):
if len(binary_rep) == 1:
op = (
PhaseShift(theta, wires[0])
if int(binary_rep)
else PauliX(wires[0]) @ PhaseShift(theta, wires[0]) @ PauliX(wires[0])
)
else:
base_op = (
PhaseShift(theta, wires[-1])
if int(binary_rep[-1])
else PauliX(wires[-1]) @ PhaseShift(theta, wires[-1]) @ PauliX(wires[-1])
)
op = qml.ctrl(
base_op, control=wires[:-1], control_values=[int(i) for i in binary_rep[:-1]]
)
return op

n_log2 = int(np.log2(n))
positive_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k)]
negative_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k, n)]

positive_ops = [
_get_op_from_binary_rep(br, phi, wires=wires) for br in positive_binary_reps
]
negative_ops = [
_get_op_from_binary_rep(br, -1 * phi, wires=wires) for br in negative_binary_reps
]

return positive_ops + negative_ops

"""Computes the adjoint of the operator."""
phi = self.parameters[0]
dim, _ = self.hyperparameters["dimension"]
return PCPhase(-1 * phi, dim=dim, wires=self.wires)

[docs]    def pow(self, z):
"""Computes the operator raised to z."""
phi = self.parameters[0]
dim, _ = self.hyperparameters["dimension"]
return [PCPhase(phi * z, dim=dim, wires=self.wires)]

[docs]    def simplify(self):
"""Simplifies the operator if possible."""
phi = self.parameters[0] % (2 * np.pi)
dim, _ = self.hyperparameters["dimension"]

if _can_replace(phi, 0):
return qml.Identity(wires=self.wires[0])

return PCPhase(phi, dim=dim, wires=self.wires)

[docs]    def label(self, decimals=None, base_label=None, cache=None):
"""The label of the operator when displayed in a circuit."""
return super().label(decimals=decimals, base_label=base_label or "∏_ϕ", cache=cache)

[docs]class IsingXX(Operation):
r"""
Ising XX coupling gate

.. math:: XX(\phi) = \exp(-i \frac{\phi}{2} (X \otimes X)) =
\begin{bmatrix} =
\cos(\phi / 2) & 0 & 0 & -i \sin(\phi / 2) \\
0 & \cos(\phi / 2) & -i \sin(\phi / 2) & 0 \\
0 & -i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\
-i \sin(\phi / 2) & 0 & 0 & \cos(\phi / 2)
\end{bmatrix}.

.. note::

Special cases of using the :math:XX operator include:

* :math:XX(0) = I;
* :math:XX(\pi) = i (X \otimes X).

**Details:**

* Number of wires: 2
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: :math:\frac{d}{d\phi}f(XX(\phi)) = \frac{1}{2}\left[f(XX(\phi +\pi/2)) - f(XX(\phi-\pi/2))\right]
where :math:f is an expectation value depending on :math:XX(\phi).

Args:
phi (float): the phase angle
wires (int): the subsystem the gate acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = 2
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

parameter_frequencies = [(1,)]

[docs]    def generator(self):
return -0.5 * PauliX(wires=self.wires[0]) @ PauliX(wires=self.wires[1])

def __init__(self, phi, wires, do_queue=True, id=None):
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_matrix(phi):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.

.. seealso:: :meth:~.IsingXX.matrix

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.IsingXX.compute_matrix(torch.tensor(0.5))
tensor([[0.9689+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000-0.2474j],
[0.0000+0.0000j, 0.9689+0.0000j, 0.0000-0.2474j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000-0.2474j, 0.9689+0.0000j, 0.0000+0.0000j],
[0.0000-0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.0000j]],
dtype=torch.complex128)
"""
c = qml.math.cos(phi / 2)
s = qml.math.sin(phi / 2)

eye = qml.math.eye(4, like=phi)
rev_eye = qml.math.convert_like(np.eye(4)[::-1].copy(), phi)
if qml.math.get_interface(phi) == "tensorflow":
c = qml.math.cast_like(c, 1j)
s = qml.math.cast_like(s, 1j)
eye = qml.math.cast_like(eye, 1j)
rev_eye = qml.math.cast_like(rev_eye, 1j)

# The following avoids casting an imaginary quantity to reals when backpropagating
js = -1j * s
if qml.math.ndim(phi) == 0:
return c * eye + js * rev_eye

return qml.math.tensordot(c, eye, axes=0) + qml.math.tensordot(js, rev_eye, axes=0)

[docs]    @staticmethod
def compute_decomposition(phi, wires):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.IsingXX.decomposition.

Args:
phi (float): the phase angle
wires (Iterable, Wires): the subsystem the gate acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.IsingXX.compute_decomposition(1.23, wires=(0,1))
[CNOT(wires=[0, 1]), RX(1.23, wires=[0]), CNOT(wires=[0, 1]]

"""
decomp_ops = [
qml.CNOT(wires=wires),
RX(phi, wires=[wires[0]]),
qml.CNOT(wires=wires),
]
return decomp_ops

(phi,) = self.parameters
return IsingXX(-phi, wires=self.wires)

[docs]    def pow(self, z):
return [IsingXX(self.data[0] * z, wires=self.wires)]

[docs]    def simplify(self):
phi = self.data[0] % (4 * np.pi)

if _can_replace(phi, 0):
return qml.Identity(wires=self.wires[0])

return IsingXX(phi, wires=self.wires)

[docs]class IsingYY(Operation):
r"""
Ising YY coupling gate

.. math:: \mathtt{YY}(\phi) = \exp(-i \frac{\phi}{2} (Y \otimes Y)) =
\begin{bmatrix}
\cos(\phi / 2) & 0 & 0 & i \sin(\phi / 2) \\
0 & \cos(\phi / 2) & -i \sin(\phi / 2) & 0 \\
0 & -i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\
i \sin(\phi / 2) & 0 & 0 & \cos(\phi / 2)
\end{bmatrix}.

.. note::

Special cases of using the :math:YY operator include:

* :math:YY(0) = I;
* :math:YY(\pi) = i (Y \otimes Y).

**Details:**

* Number of wires: 2
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: :math:\frac{d}{d\phi}f(YY(\phi)) = \frac{1}{2}\left[f(YY(\phi +\pi/2)) - f(YY(\phi-\pi/2))\right]
where :math:f is an expectation value depending on :math:YY(\phi).

Args:
phi (float): the phase angle
wires (int): the subsystem the gate acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = 2
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

parameter_frequencies = [(1,)]

[docs]    def generator(self):
return -0.5 * PauliY(wires=self.wires[0]) @ PauliY(wires=self.wires[1])

def __init__(self, phi, wires, do_queue=True, id=None):
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_decomposition(phi, wires):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.IsingYY.decomposition.

Args:
phi (float): the phase angle
wires (Iterable, Wires): the subsystem the gate acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.IsingYY.compute_decomposition(1.23, wires=(0,1))
[CY(wires=[0, 1]), RY(1.23, wires=[0]), CY(wires=[0, 1])]

"""
return [
qml.CY(wires=wires),
RY(phi, wires=[wires[0]]),
qml.CY(wires=wires),
]

[docs]    @staticmethod
def compute_matrix(phi):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.IsingYY.matrix

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.IsingYY.compute_matrix(torch.tensor(0.5))
tensor([[0.9689+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.2474j],
[0.0000+0.0000j, 0.9689+0.0000j, 0.0000-0.2474j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000-0.2474j, 0.9689+0.0000j, 0.0000+0.0000j],
[0.0000+0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.0000j]])
"""
c = qml.math.cos(phi / 2)
s = qml.math.sin(phi / 2)

if qml.math.get_interface(phi) == "tensorflow":
c = qml.math.cast_like(c, 1j)
s = qml.math.cast_like(s, 1j)

js = 1j * s
r_term = qml.math.cast_like(
qml.math.array(
[
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, -1.0, 0.0],
[0.0, -1.0, 0.0, 0.0],
[1.0, 0.0, 0.0, 0.0],
],
like=js,
),
1j,
)
if qml.math.ndim(phi) == 0:
return c * qml.math.cast_like(qml.math.eye(4, like=c), c) + js * r_term

return qml.math.tensordot(c, np.eye(4), axes=0) + qml.math.tensordot(js, r_term, axes=0)

(phi,) = self.parameters
return IsingYY(-phi, wires=self.wires)

[docs]    def pow(self, z):
return [IsingYY(self.data[0] * z, wires=self.wires)]

[docs]    def simplify(self):
phi = self.data[0] % (4 * np.pi)

if _can_replace(phi, 0):
return qml.Identity(wires=self.wires[0])

return IsingYY(phi, wires=self.wires)

[docs]class IsingZZ(Operation):
r"""
Ising ZZ coupling gate

.. math:: ZZ(\phi) = \exp(-i \frac{\phi}{2} (Z \otimes Z)) =
\begin{bmatrix}
e^{-i \phi / 2} & 0 & 0 & 0 \\
0 & e^{i \phi / 2} & 0 & 0 \\
0 & 0 & e^{i \phi / 2} & 0 \\
0 & 0 & 0 & e^{-i \phi / 2}
\end{bmatrix}.

.. note::

Special cases of using the :math:ZZ operator include:

* :math:ZZ(0) = I;
* :math:ZZ(\pi) = - (Z \otimes Z);
* :math:ZZ(2\pi) = - I;

**Details:**

* Number of wires: 2
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: :math:\frac{d}{d\phi}f(ZZ(\phi)) = \frac{1}{2}\left[f(ZZ(\phi +\pi/2)) - f(ZZ(\phi-\pi/2))\right]
where :math:f is an expectation value depending on :math:ZZ(\theta).

Args:
phi (float): the phase angle
wires (int): the subsystem the gate acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = 2
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

parameter_frequencies = [(1,)]

[docs]    def generator(self):
return -0.5 * PauliZ(wires=self.wires[0]) @ PauliZ(wires=self.wires[1])

def __init__(self, phi, wires, do_queue=True, id=None):
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_decomposition(phi, wires):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.IsingZZ.decomposition.

Args:
phi (float): the phase angle
wires (Iterable, Wires): the subsystem the gate acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.IsingZZ.compute_decomposition(1.23, wires=[0, 1])
[CNOT(wires=[0, 1]), RZ(1.23, wires=[1]), CNOT(wires=[0, 1])]

"""
return [
qml.CNOT(wires=wires),
RZ(phi, wires=[wires[1]]),
qml.CNOT(wires=wires),
]

[docs]    @staticmethod
def compute_matrix(phi):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.IsingZZ.matrix

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.IsingZZ.compute_matrix(torch.tensor(0.5))
tensor([[0.9689-0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.9689+0.2474j, 0.0000+0.0000j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.2474j, 0.0000+0.0000j],
[0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689-0.2474j]])
"""
if qml.math.get_interface(phi) == "tensorflow":
p = qml.math.exp(-0.5j * qml.math.cast_like(phi, 1j))
if qml.math.ndim(p) == 0:
return qml.math.diag([p, qml.math.conj(p), qml.math.conj(p), p])

diags = stack_last([p, qml.math.conj(p), qml.math.conj(p), p])
return diags[:, :, np.newaxis] * qml.math.cast_like(qml.math.eye(4, like=diags), diags)

signs = qml.math.array([1, -1, -1, 1], like=phi)
arg = -0.5j * phi

if qml.math.ndim(arg) == 0:
return qml.math.diag(qml.math.exp(arg * signs))

diags = qml.math.exp(qml.math.outer(arg, signs))
return diags[:, :, np.newaxis] * qml.math.cast_like(qml.math.eye(4, like=diags), diags)

[docs]    @staticmethod
def compute_eigvals(phi):  # pylint: disable=arguments-differ
r"""Eigenvalues of the operator in the computational basis (static method).

If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger},
the operator can be reconstructed as

.. math:: O = U \Sigma U^{\dagger},

where :math:\Sigma is the diagonal matrix containing the eigenvalues.

Otherwise, no particular order for the eigenvalues is guaranteed.

.. seealso:: :meth:~.IsingZZ.eigvals

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: eigenvalues

**Example**

>>> qml.IsingZZ.compute_eigvals(torch.tensor(0.5))
tensor([0.9689-0.2474j, 0.9689+0.2474j, 0.9689+0.2474j, 0.9689-0.2474j])
"""
if qml.math.get_interface(phi) == "tensorflow":
phase = qml.math.exp(-0.5j * qml.math.cast_like(phi, 1j))
return stack_last([phase, qml.math.conj(phase), qml.math.conj(phase), phase])

prefactors = qml.math.array([-0.5j, 0.5j, 0.5j, -0.5j], like=phi)
if qml.math.ndim(phi) == 0:
product = phi * prefactors
else:
product = qml.math.outer(phi, prefactors)
return qml.math.exp(product)

(phi,) = self.parameters
return IsingZZ(-phi, wires=self.wires)

[docs]    def pow(self, z):
return [IsingZZ(self.data[0] * z, wires=self.wires)]

[docs]    def simplify(self):
phi = self.data[0] % (4 * np.pi)

if _can_replace(phi, 0):
return qml.Identity(wires=self.wires[0])

return IsingZZ(phi, wires=self.wires)

[docs]class IsingXY(Operation):
r"""
Ising (XX + YY) coupling gate

.. math:: \mathtt{XY}(\phi) = \exp(i \frac{\theta}{4} (X \otimes X + Y \otimes Y)) =
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & \cos(\phi / 2) & i \sin(\phi / 2) & 0 \\
0 & i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}.

.. note::

Special cases of using the :math:XY operator include:

* :math:XY(0) = I;
* :math:XY(\frac{\pi}{2}) = \sqrt{iSWAP};
* :math:XY(\pi) = iSWAP;

**Details:**

* Number of wires: 2
* Number of parameters: 1
* Number of dimensions per parameter: (0,)
* Gradient recipe: The XY operator satisfies a four-term parameter-shift rule

.. math::
\frac{d}{d \phi} f(XY(\phi))
= c_+ \left[ f(XY(\phi + a)) - f(XY(\phi - a)) \right]
- c_- \left[ f(XY(\phi + b)) - f(XY(\phi - b)) \right]

where :math:f is an expectation value depending on :math:XY(\phi), and

- :math:a = \pi / 2
- :math:b = 3 \pi / 2
- :math:c_{\pm} = (\sqrt{2} \pm 1)/{4 \sqrt{2}}

Args:
phi (float): the phase angle
wires (int): the subsystem the gate acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = 2
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

ndim_params = (0,)
"""tuple[int]: Number of dimensions per trainable parameter that the operator depends on."""

parameter_frequencies = [(0.5, 1.0)]

[docs]    def generator(self):
return 0.25 * (
PauliX(wires=self.wires[0]) @ PauliX(wires=self.wires[1])
+ PauliY(wires=self.wires[0]) @ PauliY(wires=self.wires[1])
)

def __init__(self, phi, wires, do_queue=True, id=None):
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_decomposition(phi, wires):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.IsingXY.decomposition.

Args:
phi (float): the phase angle
wires (Iterable, Wires): the subsystem the gate acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.IsingXY.compute_decomposition(1.23, wires=(0,1))

"""
return [
qml.CY(wires=wires),
RY(phi / 2, wires=[wires[0]]),
RX(-phi / 2, wires=[wires[1]]),
qml.CY(wires=wires),
]

[docs]    @staticmethod
def compute_matrix(phi):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.IsingXY.matrix

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.IsingXY.compute_matrix(0.5)
array([[1.        +0.j        , 0.        +0.j        ,        0.        +0.j        , 0.        +0.j        ],
[0.        +0.j        , 0.96891242+0.j        ,        0.        +0.24740396j, 0.        +0.j        ],
[0.        +0.j        , 0.        +0.24740396j,        0.96891242+0.j        , 0.        +0.j        ],
[0.        +0.j        , 0.        +0.j        ,        0.        +0.j        , 1.        +0.j        ]])
"""
c = qml.math.cos(phi / 2)
s = qml.math.sin(phi / 2)

if qml.math.get_interface(phi) == "tensorflow":
c = qml.math.cast_like(c, 1j)
s = qml.math.cast_like(s, 1j)

js = 1j * s
off_diag = qml.math.cast_like(
qml.math.array(
[
[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0],
],
like=js,
),
1j,
)
if qml.math.ndim(phi) == 0:
return qml.math.diag([1, c, c, 1]) + js * off_diag

ones = qml.math.ones_like(c)
diags = stack_last([ones, c, c, ones])[:, :, np.newaxis]
return diags * np.eye(4) + qml.math.tensordot(js, off_diag, axes=0)

[docs]    @staticmethod
def compute_eigvals(phi):  # pylint: disable=arguments-differ
r"""Eigenvalues of the operator in the computational basis (static method).

If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger},
the operator can be reconstructed as

.. math:: O = U \Sigma U^{\dagger},

where :math:\Sigma is the diagonal matrix containing the eigenvalues.

Otherwise, no particular order for the eigenvalues is guaranteed.

.. seealso:: :meth:~.IsingXY.eigvals

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: eigenvalues

**Example**

>>> qml.IsingXY.compute_eigvals(0.5)
array([0.96891242+0.24740396j, 0.96891242-0.24740396j,       1.        +0.j        , 1.        +0.j        ])
"""
if qml.math.get_interface(phi) == "tensorflow":
phi = qml.math.cast_like(phi, 1j)

signs = np.array([1, -1, 0, 0])
if qml.math.ndim(phi) == 0:
return qml.math.exp(0.5j * phi * signs)

return qml.math.exp(qml.math.tensordot(0.5j * phi, signs, axes=0))

(phi,) = self.parameters
return IsingXY(-phi, wires=self.wires)

[docs]    def pow(self, z):
return [IsingXY(self.data[0] * z, wires=self.wires)]

[docs]    def simplify(self):
phi = self.data[0] % (4 * np.pi)

if _can_replace(phi, 0):
return qml.Identity(wires=self.wires[0])

return IsingXY(phi, wires=self.wires)

[docs]class PSWAP(Operation):
r"""Phase SWAP gate

.. math:: PSWAP(\phi) = \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & e^{i \phi} & 0 \\
0 & e^{i \phi} & 0 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}.

**Details:**

* Number of wires: 2
* Number of parameters: 1

.. math::
\frac{d}{d \phi} PSWAP(\phi)
= \frac{1}{2} \left[ PSWAP(\phi + \pi / 2) - PSWAP(\phi - \pi / 2) \right]

Args:
phi (float): the phase angle
wires (int): the subsystem the gate acts on
do_queue (bool): Indicates whether the operator should be
immediately pushed into the Operator queue (optional)
id (str or None): String representing the operation (optional)
"""
num_wires = 2
num_params = 1
"""int: Number of trainable parameters that the operator depends on."""

grad_recipe = ([[0.5, 1, np.pi / 2], [-0.5, 1, -np.pi / 2]],)

def __init__(self, phi, wires, do_queue=True, id=None):
super().__init__(phi, wires=wires, do_queue=do_queue, id=id)

[docs]    @staticmethod
def compute_decomposition(phi, wires):
r"""Representation of the operator as a product of other operators (static method). :

.. math:: O = O_1 O_2 \dots O_n.

.. seealso:: :meth:~.PSWAP.decomposition.

Args:
phi (float): the phase angle
wires (Iterable, Wires): the subsystem the gate acts on

Returns:
list[Operator]: decomposition into lower level operations

**Example:**

>>> qml.PSWAP.compute_decomposition(1.23, wires=(0,1))
[SWAP(wires=[0, 1]), CNOT(wires=[0, 1]), PhaseShift(1.23, wires=[1]), CNOT(wires=[0, 1])]
"""
return [
qml.SWAP(wires=wires),
qml.CNOT(wires=wires),
PhaseShift(phi, wires=[wires[1]]),
qml.CNOT(wires=wires),
]

[docs]    @staticmethod
def compute_matrix(phi):  # pylint: disable=arguments-differ
r"""Representation of the operator as a canonical matrix in the computational basis (static method).

The canonical matrix is the textbook matrix representation that does not consider wires.
Implicitly, this assumes that the wires of the operator correspond to the global wire order.

.. seealso:: :meth:~.PSWAP.matrix

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: canonical matrix

**Example**

>>> qml.PSWAP.compute_matrix(0.5)
array([[1.        +0.j, 0.        +0.j        , 0.        +0.j        , 0.        +0.j],
[0.        +0.j, 0.        +0.j        , 0.87758256+0.47942554j, 0.        +0.j],
[0.        +0.j, 0.87758256+0.47942554j, 0.        +0.j        , 0.        +0.j],
[0.        +0.j, 0.        +0.j        , 0.        +0.j        , 1.        +0.j]])
"""
if qml.math.get_interface(phi) == "tensorflow":
phi = qml.math.cast_like(phi, 1j)

e = qml.math.exp(1j * phi)

return qml.math.stack(
[
stack_last([1, 0, 0, 0]),
stack_last([0, 0, e, 0]),
stack_last([0, e, 0, 0]),
stack_last([0, 0, 0, 1]),
],
axis=-2,
)

[docs]    @staticmethod
def compute_eigvals(phi):  # pylint: disable=arguments-differ
r"""Eigenvalues of the operator in the computational basis (static method).

If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger},
the operator can be reconstructed as

.. math:: O = U \Sigma U^{\dagger},

where :math:\Sigma is the diagonal matrix containing the eigenvalues.

Otherwise, no particular order for the eigenvalues is guaranteed.

.. seealso:: :meth:~.PSWAP.eigvals

Args:
phi (tensor_like or float): phase angle

Returns:
tensor_like: eigenvalues

**Example**

>>> qml.PSWAP.compute_eigvals(0.5)
array([ 1.        +0.j        ,  1.        +0.j,       -0.87758256-0.47942554j,  0.87758256+0.47942554j])
"""
if qml.math.get_interface(phi) == "tensorflow":
phi = qml.math.cast_like(phi, 1j)

return qml.math.stack([1, 1, -qml.math.exp(1j * phi), qml.math.exp(1j * phi)])

(phi,) = self.parameters
return PSWAP(-phi, wires=self.wires)

[docs]    def simplify(self):
phi = self.data[0] % (2 * np.pi)

if _can_replace(phi, 0):
return qml.SWAP(wires=self.wires)

return PSWAP(phi, wires=self.wires)


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