qml.operation.Operator¶

class
Operator
(*params, wires=None, id=None)[source]¶ Bases:
abc.ABC
Base class representing quantum operators.
Operators are uniquely defined by their name, the wires they act on, their (trainable) parameters, and their (nontrainable) hyperparameters. The trainable parameters can be tensors of any supported autodifferentiation framework.
An operator can define any of the following representations:
Representation as a matrix (
Operator.matrix()
), as specified by a global wire order that tells us where the wires are found on a register.Representation as a sparse matrix (
Operator.sparse_matrix()
). Currently, this is a SciPy CSR matrix format.Representation via the eigenvalue decomposition specified by eigenvalues (
Operator.eigvals()
) and diagonalizing gates (Operator.diagonalizing_gates()
).Representation as a product of operators (
Operator.decomposition()
).Representation as a linear combination of operators (
Operator.terms()
).Representation by a generator via \(e^{G}\) (
Operator.generator()
).
Each representation method comes with a static method prefixed by
compute_
, which takes the signature(*parameters, **hyperparameters)
(for numerical representations that do not need to know about wire labels) or(*parameters, wires, **hyperparameters)
, whereparameters
,wires
, andhyperparameters
are the respective attributes of the operator class. Parameters
*params (tuple[tensor_like]) – trainable parameters
wires (Iterable[Any] or Any) – Wire label(s) that the operator acts on. If not given, args[1] is interpreted as wires.
id (str) – custom label given to an operator instance, can be useful for some applications where the instance has to be identified
Example
A custom operator can be created by inheriting from
Operator
or one of its subclasses.The following is an example for a custom gate that inherits from the
Operation
subclass. It acts by potentially flipping a qubit and rotating another qubit. The custom operator defines a decomposition, which the devices can use (since it is unlikely that a device knows a native implementation forFlipAndRotate
). It also defines an adjoint operator.import pennylane as qml class FlipAndRotate(qml.operation.Operation): # Define how many wires the operator acts on in total. # In our case this may be one or two, which is why we # use the AnyWires Enumeration to indicate a variable number. num_wires = qml.operation.AnyWires # This attribute tells PennyLane what differentiation method to use. Here # we request parametershift (or "analytic") differentiation. grad_method = "A" def __init__(self, angle, wire_rot, wire_flip=None, do_flip=False, id=None): # checking the inputs  if do_flip and wire_flip is None: raise ValueError("Expected a wire to flip; got None.") # # do_flip is not trainable but influences the action of the operator, # which is why we define it to be a hyperparameter self._hyperparameters = { "do_flip": do_flip } # we extract all wires that the operator acts on, # relying on the Wire class arithmetic all_wires = qml.wires.Wires(wire_rot) + qml.wires.Wires(wire_flip) # The parent class expects all trainable parameters to be fed as positional # arguments, and all wires acted on fed as a keyword argument. # The id keyword argument allows users to give their instance a custom name. super().__init__(angle, wires=all_wires, id=id) @property def num_params(self): # if it is known before creation, define the number of parameters to expect here, # which makes sure an error is raised if the wrong number was passed. The angle # parameter is the only trainable parameter of the operation return 1 @property def ndim_params(self): # if it is known before creation, define the number of dimensions each parameter # is expected to have. This makes sure to raise an error if a wronglyshaped # parameter was passed. The angle parameter is expected to be a scalar return (0,) @staticmethod def compute_decomposition(angle, wires, do_flip): # pylint: disable=argumentsdiffer # Overwriting this method defines the decomposition of the new gate, as it is # called by Operator.decomposition(). # The general signature of this function is (*parameters, wires, **hyperparameters). op_list = [] if do_flip: op_list.append(qml.X(wires[1])) op_list.append(qml.RX(angle, wires=wires[0])) return op_list def adjoint(self): # the adjoint operator of this gate simply negates the angle return FlipAndRotate(self.parameters[0], self.wires[0], self.wires[1], do_flip=self.hyperparameters["do_flip"])
We can use the operation as follows:
from pennylane import numpy as np dev = qml.device("default.qubit", wires=["q1", "q2", "q3"]) @qml.qnode(dev) def circuit(angle): FlipAndRotate(angle, wire_rot="q1", wire_flip="q1") return qml.expval(qml.Z("q1"))
>>> a = np.array(3.14) >>> circuit(a) tensor(0.99999873, requires_grad=True)
Serialization and Pytree format
PennyLane operations are automatically registered as Pytrees .
For most operators, this process will happen automatically without need for custom implementations.
Customization of this process must occur if:
The data and hyperparameters are insufficient to reproduce the original operation via its initialization
The hyperparameters contain a nonhashable component, such as a list or dictionary.
Some examples include arithmetic operators, like
Adjoint
orSum
, or templates that perform preprocessing during initialization.See the
Operator._flatten
andOperator._unflatten
methods for more information.>>> op = qml.PauliRot(1.2, "XY", wires=(0,1)) >>> op._flatten() ((1.2,), (<Wires = [0, 1]>, (('pauli_word', 'XY'),))) >>> qml.PauliRot._unflatten(*op._flatten()) PauliRot(1.2, XY, wires=[0, 1])
Parameter broadcasting
Many quantum functions are executed repeatedly at different parameters, which can be done with parameter broadcasting. For usage details and examples see the
QNode
documentation.In order to support parameter broadcasting with an operator class, the following steps are necessary:
Define the class attribute
ndim_params
, a tuple that indicates the expected number of dimensions for each operator argument without broadcasting. For example,FlipAndRotate
above hasndim_params = (0,)
for a single scalar argument. An operator taking a matrix argument and a scalar would havendim_params = (2, 0)
. Note thatndim_params
does not require the size of the axes.Make the representations of the operator broadcastingcompatible. Typically, one or multiple of the methods
compute_matrix
,compute_eigvals
andcompute_decomposition
are defined by an operator, and these need to work with the original input and output as well as with broadcasted inputs and outputs that have an additional, leading axis. See below for an example.Make sure that validation within the above representation methods and
__init__
—if it is overwritten by the operator class—allow for broadcasted inputs. For custom operators this usually is a minor step or not necessary at all.For proper registration, add the name of the operator to
supports_broadcasting
in the filepennylane/ops/qubit/attributes.py
.Make sure that the operator’s
_check_batching
method is called in all places required. This is typically done automatically but needs to be assured. See further below for details.
Examples
Consider an operator with the same matrix as
qml.RX
. A basic variant ofcompute_matrix
(which will not be compatible with all autodifferentiation frameworks or backpropagation) is@staticmethod def compute_matrix(theta): '''Broadcasting axis ends up in the wrong position.''' c = qml.math.cos(theta / 2) s = qml.math.sin(theta / 2) return qml.math.array([[c, 1j * s], [1j * s, c]])
If we passed a broadcasted argument
theta
of shape(batch_size,)
to this method, which would have one instead of zero dimensions,cos
andsin
would correctly be applied elementwise. We would also obtain the correct matrix with shape(2, 2, batch_size)
. However, the broadcasting axis needs to be the first axis by convention, so that we need to move the broadcasting axis–if it exists–to the front before returning the matrix:@staticmethod def compute_matrix(theta): '''Broadcasting axis ends up in the correct leading position.''' c = qml.math.cos(theta / 2) s = qml.math.sin(theta / 2) mat = qml.math.array([[c, 1j * s], [1j * s, c]]) # Check whether the input has a broadcasting axis if qml.math.ndim(theta)==1: # Move the broadcasting axis to the first position return qml.math.moveaxis(mat, 2, 0) return mat
Adapting
compute_eigvals
to broadcasting looks similar.Usually no major changes are required for
compute_decomposition
, but we need to take care of the correct mapping of input arguments to the operators in the decomposition. As an example, consider the operator that represents a layer ofRX
rotations with individual angles for each rotation. Without broadcasting, it takes one onedimensional array, i.e.ndim_params=(1,)
. Its decomposition, which is a convenient way to support this custom operation on all devices that implementRX
, might look like this:@staticmethod def compute_decomposition(theta, wires): '''Iterate over the first axis of theta.''' decomp_ops = [qml.RX(x, wires=w) for x, w in zip(theta, wires)] return decomp_ops
If
theta
is a broadcasted argument, its first axis is the broadcasting axis and we would like to iterate over the second axis within thefor
loop instead. This is easily achieved by adding a transposition oftheta
that switches the axes in this case. Conveniently this does not have any effect in the nonbroadcasted case, so that we do not need to handle two cases separately.@staticmethod def compute_decomposition(theta, wires): '''Iterate over the last axis of theta, which is also the first axis or the second axis without and with broadcasting, respectively.''' decomp_ops = [qml.RX(x, wires=w) for x, w in zip(qml.math.T(theta), wires)] return decomp_ops
The ``_check_batching`` method
Each operator determines whether it is used with a batch of parameters within the
_check_batching
method, by comparing the shape of the input data to the expected shape. Therefore, it is necessary to call_check_batching
on any new input parameters passed to the operator. By default, any class inheriting fromOperator
will do so the first time itsbatch_size
property is accessed._check_batching
modifies the following instance attributes:_ndim_params
: The number of dimensions of the parameters passed to_check_batching
. For anOperator
that does _not_ set thendim_params
attribute,_ndim_params
is used as a surrogate, interpreting any parameters as “not broadcasted”. This attribute should be understood as temporary and likely should not be used in other contexts._batch_size
: If theOperator
is broadcasted: The batch size/size of the broadcasting axis. If it is not broadcasted:None
. AnOperator
that does not support broadcasting will report to not be broadcasted independently of the input.
These two properties are defined lazily, and accessing the public version of either one of them (in other words, without the leading underscore) for the first time will trigger a call to
_check_batching
, which validates and sets these properties.Attributes
Arithmetic depth of the operator.
Batch size of the operator if it is used with broadcasted parameters.
Integer hash that uniquely represents the operator.
Dictionary of nontrainable variables that this operation depends on.
Custom string to label a specific operator instance.
This property determines if an operator is hermitian.
String for the name of the operator.
Number of dimensions per trainable parameter of the operator.
Number of trainable parameters that the operator depends on.
Number of wires the operator acts on.
Trainable parameters that the operator depends on.
A
PauliSentence
representation of the Operator, orNone
if it doesn’t have one.Wires that the operator acts on.

arithmetic_depth
¶ Arithmetic depth of the operator.

batch_size
¶ Batch size of the operator if it is used with broadcasted parameters.
The
batch_size
is determined based onndim_params
and the provided parameters for the operator. If (some of) the latter have an additional dimension, and this dimension has the same size for all parameters, its size is the batch size of the operator. If no parameter has an additional dimension, the batch size isNone
. Returns
Size of the parameter broadcasting dimension if present, else
None
. Return type
int or None

has_adjoint
= False¶

has_decomposition
= False¶

has_diagonalizing_gates
= False¶

has_generator
= False¶

has_matrix
= False¶

hash
¶ Integer hash that uniquely represents the operator.
 Type
int

hyperparameters
¶ Dictionary of nontrainable variables that this operation depends on.
 Type
dict

id
¶ Custom string to label a specific operator instance.

is_hermitian
¶ This property determines if an operator is hermitian.

name
¶ String for the name of the operator.

ndim_params
¶ Number of dimensions per trainable parameter of the operator.
By default, this property returns the numbers of dimensions of the parameters used for the operator creation. If the parameter sizes for an operator subclass are fixed, this property can be overwritten to return the fixed value.
 Returns
Number of dimensions for each trainable parameter.
 Return type
tuple

num_params
¶ Number of trainable parameters that the operator depends on.
By default, this property returns as many parameters as were used for the operator creation. If the number of parameters for an operator subclass is fixed, this property can be overwritten to return the fixed value.
 Returns
number of parameters
 Return type
int

num_wires
= 1¶ Number of wires the operator acts on.

parameters
¶ Trainable parameters that the operator depends on.

pauli_rep
¶ A
PauliSentence
representation of the Operator, orNone
if it doesn’t have one.
Methods
adjoint
()Create an operation that is the adjoint of this one.
compute_decomposition
(*params[, wires])Representation of the operator as a product of other operators (static method).
compute_diagonalizing_gates
(*params, wires, …)Sequence of gates that diagonalize the operator in the computational basis (static method).
compute_eigvals
(*params, **hyperparams)Eigenvalues of the operator in the computational basis (static method).
compute_matrix
(*params, **hyperparams)Representation of the operator as a canonical matrix in the computational basis (static method).
compute_sparse_matrix
(*params, **hyperparams)Representation of the operator as a sparse matrix in the computational basis (static method).
Representation of the operator as a product of other operators.
Sequence of gates that diagonalize the operator in the computational basis.
eigvals
()Eigenvalues of the operator in the computational basis.
expand
()Returns a tape that contains the decomposition of the operator.
Generator of an operator that is in singleparameterform.
label
([decimals, base_label, cache])A customizable string representation of the operator.
map_wires
(wire_map)Returns a copy of the current operator with its wires changed according to the given wire map.
matrix
([wire_order])Representation of the operator as a matrix in the computational basis.
pow
(z)A list of new operators equal to this one raised to the given power.
queue
([context])Append the operator to the Operator queue.
simplify
()Reduce the depth of nested operators to the minimum.
sparse_matrix
([wire_order])Representation of the operator as a sparse matrix in the computational basis.
terms
()Representation of the operator as a linear combination of other operators.

adjoint
()[source]¶ Create an operation that is the adjoint of this one.
Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.
 Returns
The adjointed operation.

static
compute_decomposition
(*params, wires=None, **hyperparameters)[source]¶ Representation of the operator as a product of other operators (static method).
\[O = O_1 O_2 \dots O_n.\]Note
Operations making up the decomposition should be queued within the
compute_decomposition
method.See also
 Parameters
*params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
**hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
decomposition of the operator
 Return type
list[Operator]

static
compute_diagonalizing_gates
(*params, wires, **hyperparams)[source]¶ Sequence of gates that diagonalize the operator in the computational basis (static method).
Given the eigendecomposition \(O = U \Sigma U^{\dagger}\) where \(\Sigma\) is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary \(U^{\dagger}\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
list of diagonalizing gates
 Return type
list[Operator]

static
compute_eigvals
(*params, **hyperparams)[source]¶ Eigenvalues of the operator in the computational basis (static method).
If
diagonalizing_gates
are specified and implement a unitary \(U^{\dagger}\), the operator can be reconstructed as\[O = U \Sigma U^{\dagger},\]where \(\Sigma\) is the diagonal matrix containing the eigenvalues.
Otherwise, no particular order for the eigenvalues is guaranteed.
See also
 Parameters
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
eigenvalues
 Return type
tensor_like

static
compute_matrix
(*params, **hyperparams)[source]¶ 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.
See also
 Parameters
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
matrix representation
 Return type
tensor_like

static
compute_sparse_matrix
(*params, **hyperparams)[source]¶ Representation of the operator as a sparse 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.
See also
 Parameters
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

decomposition
()[source]¶ Representation of the operator as a product of other operators.
\[O = O_1 O_2 \dots O_n\]A
DecompositionUndefinedError
is raised if no representation by decomposition is defined.See also
 Returns
decomposition of the operator
 Return type
list[Operator]

diagonalizing_gates
()[source]¶ Sequence of gates that diagonalize the operator in the computational basis.
Given the eigendecomposition \(O = U \Sigma U^{\dagger}\) where \(\Sigma\) is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary \(U^{\dagger}\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
A
DiagGatesUndefinedError
is raised if no representation by decomposition is defined.See also
 Returns
a list of operators
 Return type
list[Operator] or None

eigvals
()[source]¶ Eigenvalues of the operator in the computational basis.
If
diagonalizing_gates
are specified and implement a unitary \(U^{\dagger}\), the operator can be reconstructed as\[O = U \Sigma U^{\dagger},\]where \(\Sigma\) is the diagonal matrix containing the eigenvalues.
Otherwise, no particular order for the eigenvalues is guaranteed.
Note
When eigenvalues are not explicitly defined, they are computed automatically from the matrix representation. Currently, this computation is not differentiable.
A
EigvalsUndefinedError
is raised if the eigenvalues have not been defined and cannot be inferred from the matrix representation.See also
 Returns
eigenvalues
 Return type
tensor_like

expand
()[source]¶ Returns a tape that contains the decomposition of the operator.
 Returns
quantum tape
 Return type

generator
()[source]¶ Generator of an operator that is in singleparameterform.
For example, for operator
\[U(\phi) = e^{i\phi (0.5 Y + Z\otimes X)}\]we get the generator
>>> U.generator() 0.5 * Y(0) + Z(0) @ X(1)
The generator may also be provided in the form of a dense or sparse Hamiltonian (using
Hermitian
andSparseHamiltonian
respectively).The default value to return is
None
, indicating that the operation has no defined generator.

label
(decimals=None, base_label=None, cache=None)[source]¶ A customizable string representation of the operator.
 Parameters
decimals=None (int) – If
None
, no parameters are included. Else, specifies how to round the parameters.base_label=None (str) – overwrite the nonparameter component of the label
cache=None (dict) – dictionary that carries information between label calls in the same drawing
 Returns
label to use in drawings
 Return type
str
Example:
>>> op = qml.RX(1.23456, wires=0) >>> op.label() "RX" >>> op.label(base_label="my_label") "my_label" >>> op = qml.RX(1.23456, wires=0, id="test_data") >>> op.label() "RX("test_data")" >>> op.label(decimals=2) "RX\n(1.23,"test_data")" >>> op.label(base_label="my_label") "my_label("test_data")" >>> op.label(decimals=2, base_label="my_label") "my_label\n(1.23,"test_data")"
If the operation has a matrixvalued parameter and a cache dictionary is provided, unique matrices will be cached in the
'matrices'
key list. The label will contain the index of the matrix in the'matrices'
list.>>> op2 = qml.QubitUnitary(np.eye(2), wires=0) >>> cache = {'matrices': []} >>> op2.label(cache=cache) 'U(M0)' >>> cache['matrices'] [tensor([[1., 0.], [0., 1.]], requires_grad=True)] >>> op3 = qml.QubitUnitary(np.eye(4), wires=(0,1)) >>> op3.label(cache=cache) 'U(M1)' >>> cache['matrices'] [tensor([[1., 0.], [0., 1.]], requires_grad=True), tensor([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]], requires_grad=True)]

map_wires
(wire_map)[source]¶ Returns a copy of the current operator with its wires changed according to the given wire map.
 Parameters
wire_map (dict) – dictionary containing the old wires as keys and the new wires as values
 Returns
new operator
 Return type

matrix
(wire_order=None)[source]¶ Representation of the operator as a matrix in the computational basis.
If
wire_order
is provided, the numerical representation considers the position of the operator’s wires in the global wire order. Otherwise, the wire order defaults to the operator’s wires.If the matrix depends on trainable parameters, the result will be cast in the same autodifferentiation framework as the parameters.
A
MatrixUndefinedError
is raised if the matrix representation has not been defined.See also
 Parameters
wire_order (Iterable) – global wire order, must contain all wire labels from the operator’s wires
 Returns
matrix representation
 Return type
tensor_like

pow
(z)[source]¶ A list of new operators equal to this one raised to the given power.
 Parameters
z (float) – exponent for the operator
 Returns
list[
Operator
]

queue
(context=<class 'pennylane.queuing.QueuingManager'>)[source]¶ Append the operator to the Operator queue.

simplify
()[source]¶ Reduce the depth of nested operators to the minimum.
 Returns
simplified operator
 Return type

sparse_matrix
(wire_order=None)[source]¶ Representation of the operator as a sparse matrix in the computational basis.
If
wire_order
is provided, the numerical representation considers the position of the operator’s wires in the global wire order. Otherwise, the wire order defaults to the operator’s wires.A
SparseMatrixUndefinedError
is raised if the sparse matrix representation has not been defined.See also
 Parameters
wire_order (Iterable) – global wire order, must contain all wire labels from the operator’s wires
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

terms
()[source]¶ Representation of the operator as a linear combination of other operators.
\[O = \sum_i c_i O_i\]A
TermsUndefinedError
is raised if no representation by terms is defined. Returns
list of coefficients \(c_i\) and list of operations \(O_i\)
 Return type
tuple[list[tensor_like or float], list[Operation]]