qml.operation.Operator¶

class
Operator
(*params, wires=None, do_queue=True, 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.
do_queue (bool) – indicates whether the operator should be recorded when created in a tape context
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, do_queue=True, 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. # The do_queue keyword argument specifies whether or not # the operator is queued when created in a tape context. super().__init__(angle, wires=all_wires, do_queue=do_queue, 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.PauliX(wires=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.PauliZ("q1"))
>>> a = np.array(3.14) >>> circuit(a) 0.9999987318946099
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.
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_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
¶ Number of wires the operator acts on.

parameters
¶ Trainable parameters that the operator depends on.
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).
compute_terms
(*params, **hyperparams)Representation of the operator as a linear combination of other operators (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 has recorded 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.
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
() → pennylane.operation.Operator[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 \(U\), 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.
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (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.
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (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
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

static
compute_terms
(*params, **hyperparams)[source]¶ Representation of the operator as a linear combination of other operators (static method).
\[O = \sum_i c_i O_i\]See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
list of coefficients and list of operations
 Return type
tuple[list[tensor_like or float], list[Operation]]

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 \(U\), 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 has recorded 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) [Y0] + (1.0) [Z0 X1]
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(decimals=2) "RX\n(1.23)" >>> op.label(base_label="my_label") "my_label" >>> op.label(decimals=2, base_label="my_label") "my_label\n(1.23)" >>> op.inv() >>> op.label() "RX⁻¹"
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)]

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) → List[pennylane.operation.Operator][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.QueuingContext'>)[source]¶ Append the operator to the Operator queue.

simplify
() → pennylane.operation.Operator[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.See also
 Returns
list of coefficients \(c_i\) and list of operations \(O_i\)
 Return type
tuple[list[tensor_like or float], list[Operation]]