ZZ¶
- class ZZ(phi, wires)[source]¶
Bases:
Operation
The Ising ZZ gate.
\[ZZ(\phi) = e^{-\frac{\phi}{2}\hat{Z}\otimes\hat{Z}}.\]Details:
Number of wires: 2
Number of parameters: 1
Gradient recipe: \(\frac{d}{d\phi}f(ZZ(\phi)) = \frac{1}{2}\left[f(ZZ(\phi+\pi/2)) - f(ZZ(\phi-\pi/2))\right]\) where \(f\) is an expectation value depending on \(ZZ(\phi)\).
- Parameters:
phi (float) – rotation angle \(\phi\)
wires (Sequence[int]) – the subsystems the operation acts on
Attributes
If inverse is requested, this is the name of the original operator to be inverted.
The target operation for controlled gates.
Batch size of the operator if it is used with broadcasted parameters.
Control wires of the operator.
Gradient recipe for the parameter-shift method.
Integer hash that uniquely represents the operator.
Dictionary of non-trainable variables that this operation depends on.
Custom string to label a specific operator instance.
Boolean determining if the inverse of the operation was requested.
This property determines if an operator is hermitian.
Name of the operator.
Number of dimensions per trainable parameter of the operator.
Returns the frequencies for each operator parameter with respect to an expectation value of the form \(\langle \psi | U(\mathbf{p})^\dagger \hat{O} U(\mathbf{p})|\psi\rangle\).
Trainable parameters that the operator depends on.
Wires that the operator acts on.
- base_name¶
If inverse is requested, this is the name of the original operator to be inverted.
- basis = None¶
The target operation for controlled gates. target operation. If not
None
, should take a value of"X"
,"Y"
, or"Z"
.For example,
X
andCNOT
havebasis = "X"
, whereasControlledPhaseShift
andRZ
havebasis = "Z"
.- Type:
str or None
- 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
- control_wires¶
Control wires of the operator.
For operations that are not controlled, this is an empty
Wires
object of length0
.- Returns:
The control wires of the operation.
- Return type:
Wires
- grad_method = 'A'¶
- grad_recipe = None¶
Gradient recipe for the parameter-shift method.
This is a tuple with one nested list per operation parameter. For parameter \(\phi_k\), the nested list contains elements of the form \([c_i, a_i, s_i]\) where \(i\) is the index of the term, resulting in a gradient recipe of
\[\frac{\partial}{\partial\phi_k}f = \sum_{i} c_i f(a_i \phi_k + s_i).\]If
None
, the default gradient recipe containing the two terms \([c_0, a_0, s_0]=[1/2, 1, \pi/2]\) and \([c_1, a_1, s_1]=[-1/2, 1, -\pi/2]\) is assumed for every parameter.- Type:
tuple(Union(list[list[float]], None)) or None
- has_matrix = False¶
- hash¶
Integer hash that uniquely represents the operator.
- Type:
int
- hyperparameters¶
Dictionary of non-trainable variables that this operation depends on.
- Type:
dict
- id¶
Custom string to label a specific operator instance.
- inverse¶
Boolean determining if the inverse of the operation was requested.
- is_hermitian¶
This property determines if an operator is hermitian.
- name¶
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 = 1¶
- num_wires = 2¶
- parameter_frequencies¶
Returns the frequencies for each operator parameter with respect to an expectation value of the form \(\langle \psi | U(\mathbf{p})^\dagger \hat{O} U(\mathbf{p})|\psi\rangle\).
These frequencies encode the behaviour of the operator \(U(\mathbf{p})\) on the value of the expectation value as the parameters are modified. For more details, please see the
pennylane.fourier
module.- Returns:
Tuple of frequencies for each parameter. Note that only non-negative frequency values are returned.
- Return type:
list[tuple[int or float]]
Example
>>> op = qml.CRot(0.4, 0.1, 0.3, wires=[0, 1]) >>> op.parameter_frequencies [(0.5, 1), (0.5, 1), (0.5, 1)]
For operators that define a generator, the parameter frequencies are directly related to the eigenvalues of the generator:
>>> op = qml.ControlledPhaseShift(0.1, wires=[0, 1]) >>> op.parameter_frequencies [(1,)] >>> gen = qml.generator(op, format="observable") >>> gen_eigvals = qml.eigvals(gen) >>> qml.gradients.eigvals_to_frequencies(tuple(gen_eigvals)) (1.0,)
For more details on this relationship, see
eigvals_to_frequencies()
.
- parameters¶
Trainable parameters that the operator depends on.
- wires¶
Wires that the operator acts on.
- Returns:
wires
- Return type:
Wires
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 (static method).
expand
()Returns a tape that has recorded the decomposition of the operator.
Generator of an operator that is in single-parameter-form.
get_parameter_shift
(idx)Multiplier and shift for the given parameter, based on its gradient recipe.
inv
()Inverts the operator.
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.
The parameters required to implement a single-qubit gate as an equivalent
Rot
gate, up to a global phase.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()¶
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.
- Parameters:
do_queue – Whether to add the adjointed gate to the context queue.
- Returns:
The adjointed operation.
- static compute_decomposition(*params, wires=None, **hyperparameters)¶
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
decomposition()
.- 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) – non-trainable 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)¶
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 \(U\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
See also
diagonalizing_gates()
.- 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) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns:
list of diagonalizing gates
- Return type:
list[.Operator]
- static compute_eigvals(*params, **hyperparams)¶
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.
See also
eigvals()
andeigvals()
- Parameters:
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns:
eigenvalues
- Return type:
tensor_like
- static compute_matrix(*params, **hyperparams)¶
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
matrix()
andmatrix()
- Parameters:
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns:
matrix representation
- Return type:
tensor_like
- static compute_sparse_matrix(*params, **hyperparams)¶
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
sparse_matrix()
- Parameters:
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – non-trainable 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)¶
Representation of the operator as a linear combination of other operators (static method).
\[O = \sum_i c_i O_i\]See also
terms()
- Parameters:
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – non-trainable 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()¶
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
compute_decomposition()
.- Returns:
decomposition of the operator
- Return type:
list[Operator]
- diagonalizing_gates()¶
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 \(U\).
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
compute_diagonalizing_gates()
.- Returns:
a list of operators
- Return type:
list[.Operator] or None
- eigvals()¶
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.
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
compute_eigvals()
- Returns:
eigenvalues
- Return type:
tensor_like
- expand()¶
Returns a tape that has recorded the decomposition of the operator.
- Returns:
quantum tape
- Return type:
.QuantumTape
- generator()¶
Generator of an operator that is in single-parameter-form.
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.
- get_parameter_shift(idx)¶
Multiplier and shift for the given parameter, based on its gradient recipe.
- Parameters:
idx (int) – parameter index within the operation
- Returns:
list of multiplier, coefficient, shift for each term in the gradient recipe
- Return type:
list[[float, float, float]]
Note that the default value for
shift
is None, which is replaced by the default shift \(\pi/2\).
- inv()¶
Inverts the operator.
This method concatenates a string to the name of the operation, to indicate that the inverse will be used for computations.
Any subsequent call of this method will toggle between the original operation and the inverse of the operation.
- Returns:
operation to be inverted
- Return type:
Operator
- label(decimals=None, base_label=None, cache=None)¶
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 non-parameter component of the label
cache=None (dict) – dictionary that caries 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 matrix-valued 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)¶
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
compute_matrix()
- 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)¶
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'>)¶
Append the operator to the Operator queue.
- single_qubit_rot_angles()¶
The parameters required to implement a single-qubit gate as an equivalent
Rot
gate, up to a global phase.- Returns:
A list of values \([\phi, \theta, \omega]\) such that \(RZ(\omega) RY(\theta) RZ(\phi)\) is equivalent to the original operation.
- Return type:
tuple[float, float, float]
- sparse_matrix(wire_order=None)¶
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.Note
The wire_order argument is currently not implemented, and using it will raise an error.
A
SparseMatrixUndefinedError
is raised if the sparse matrix representation has not been defined.See also
compute_sparse_matrix()
- 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()¶
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
compute_terms()
- Returns:
list of coefficients \(c_i\) and list of operations \(O_i\)
- Return type:
tuple[list[tensor_like or float], list[.Operation]]