GPi¶
- class GPi(phi, wires)[source]¶
Bases:
Operation
IonQ native GPi gate.
\[\begin{split}\mathtt{GPi}(\phi) = \begin{bmatrix} 0 & e^{-i \phi} \\ e^{i \phi} & 0 \end{bmatrix}.\end{split}\]Details:
Number of wires: 1
Number of parameters: 1
- Parameters:
phi (float) – the phase angle
wires (int) – the subsystem the gate acts on
id (str or None) – String representing the operation (optional)
Attributes
Arithmetic depth of the operator.
The basis of an operation, or for controlled gates, of the target operation.
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.
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 wires the operator acts on.
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.
- arithmetic_depth¶
Arithmetic depth of the operator.
- basis¶
The basis of an operation, or for controlled gates, of the 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 = 'F'¶
- 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_adjoint = True¶
- has_decomposition = False¶
- has_diagonalizing_gates = False¶
- has_generator = False¶
- has_matrix = True¶
- 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.
- 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 = 1¶
- num_wires = 1¶
Number of wires the operator acts on.
- 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
(phi)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 single-parameter-form.
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.
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.
validate_subspace
(subspace)Validate the subspace for qutrit operations.
- 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)¶
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 \(U^{\dagger}\).
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 \(U^{\dagger}\), 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
Operator.eigvals()
andqml.eigvals()
- Parameters:
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns:
eigenvalues
- Return type:
tensor_like
- static compute_matrix(phi)[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
Operator.matrix()
andqml.matrix()
- Parameters:
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (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
attribute**hyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns:
sparse matrix representation
- Return type:
scipy.sparse._csr.csr_matrix
- 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 \(U^{\dagger}\).
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
compute_diagonalizing_gates()
.- Returns:
a list of operators
- Return type:
list[.Operator] or None
- eigvals()¶
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
compute_eigvals()
- Returns:
eigenvalues
- Return type:
tensor_like
- expand()¶
Returns a tape that contains 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.
- 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 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)"
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)]
- map_wires(wire_map: dict)¶
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:
.Operator
- 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) List[Operator] ¶
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'>)¶
Append the operator to the Operator queue.
- simplify() Operator ¶
Reduce the depth of nested operators to the minimum.
- Returns:
simplified operator
- Return type:
.Operator
- 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.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.- Returns:
list of coefficients \(c_i\) and list of operations \(O_i\)
- Return type:
tuple[list[tensor_like or float], list[.Operation]]
- static validate_subspace(subspace)¶
Validate the subspace for qutrit operations.
This method determines whether a given subspace for qutrit operations is defined correctly or not. If not, a ValueError is thrown.
- Parameters:
subspace (tuple[int]) – Subspace to check for correctness