qml.ops.op_math.Controlled¶

class Controlled(base, control_wires, control_values=None, work_wires=None, id=None)[source]¶

Bases: pennylane.ops.op_math.symbolicop.SymbolicOp

Symbolic operator denoting a controlled operator.

Parameters

base (Operator) – the operator that is controlled
control_wires (Any) – The wires to control on.

Keyword Arguments

control_values (Iterable[Bool]) – The values to control on. Must be the same length as control_wires. Defaults to True for all control wires. Provided values are converted to Bool internally.
work_wires (Any) – Any auxiliary wires that can be used in the decomposition

Note

This class, Controlled, denotes a controlled version of any individual operation. ControlledOp adds Operation specific methods and properties to the more general Controlled class.

See also

ControlledOp, and ctrl()

Example

>>> base = qml.RX(1.234, 1)
>>> Controlled(base, (0, 2, 3), control_values=[True, False, True])
Controlled(RX(1.234, wires=[1]), control_wires=[0, 2, 3], control_values=[True, False, True])
>>> op = Controlled(base, 0, control_values=[0])
>>> op
Controlled(RX(1.234, wires=[1]), control_wires=[0], control_values=[0])

The operation has both standard Operator properties and Controlled specific properties:

>>> op.base
RX(1.234, wires=[1])
>>> op.data
(1.234,)
>>> op.wires
Wires([0, 1])
>>> op.control_wires
Wires([0])
>>> op.target_wires
Wires([1])

Control values are lists of booleans, indicating whether or not to control on the 0==False value or the 1==True wire.

>>> op.control_values
[0]

Provided control values are converted to booleans internally, so any “truthy” or “falsy” objects work.

>>> Controlled(base, ("a", "b", "c"), control_values=["", None, 5]).control_values
[False, False, True]

Representations for an operator are available if the base class defines them. Sparse matrices are available if the base class defines either a sparse matrix or only a dense matrix.

>>> np.set_printoptions(precision=4) # easier to read the matrix
>>> qml.matrix(op)
array([[0.8156+0.j    , 0.    -0.5786j, 0.    +0.j    , 0.    +0.j    ],
       [0.    -0.5786j, 0.8156+0.j    , 0.    +0.j    , 0.    +0.j    ],
       [0.    +0.j    , 0.    +0.j    , 1.    +0.j    , 0.    +0.j    ],
       [0.    +0.j    , 0.    +0.j    , 0.    +0.j    , 1.    +0.j    ]])
>>> qml.eigvals(op)
array([1.    +0.j    , 1.    +0.j    , 0.8156+0.5786j, 0.8156-0.5786j])
>>> print(qml.generator(op, format='observable'))
(-0.5) [Projector0 X1]
>>> op.sparse_matrix()
<4x4 sparse matrix of type '<class 'numpy.complex128'>'
            with 6 stored elements in Compressed Sparse Row format>

If the provided base matrix is an Operation, then the created object will be of type ControlledOp. This class adds some additional methods and properties to the basic Controlled class.

>>> type(op)
<class 'pennylane.ops.op_math.controlled_class.ControlledOp'>
>>> op.parameter_frequencies
[(0.5, 1.0)]

Attributes

`arithmetic_depth`	Arithmetic depth of the operator.
`base`	The base operator.
`basis`
`batch_size`	Batch size of the operator if it is used with broadcasted parameters.
`control_values`	Iterable[Bool].
`control_wires`	The control wires.
`data`	The trainable parameters
`has_adjoint`	bool(x) -> bool
`has_decomposition`	bool(x) -> bool
`has_diagonalizing_gates`	bool(x) -> bool
`has_generator`	bool(x) -> bool
`has_matrix`	bool(x) -> bool
`has_sparse_matrix`
`hash`	Integer hash that uniquely represents the operator.
`hyperparameters`	Dictionary of non-trainable variables that this operation depends on.
`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.
`num_params`	Number of trainable parameters that the operator depends on.
`num_wires`	Number of wires the operator acts on.
`parameters`	Trainable parameters that the operator depends on.
`pauli_rep`	A `PauliSentence` representation of the Operator, or `None` if it doesn't have one.
`target_wires`	The wires of the target operator.
`wires`	Wires that the operator acts on.
`work_wires`	Additional wires that can be used in the decomposition.

arithmetic_depth¶

base¶: The base operator.

basis¶

batch_size¶

control_values¶: Iterable[Bool]. For each control wire, denotes whether to control on True or False.

control_wires¶: The control wires.

data¶: The trainable parameters

has_adjoint¶

has_decomposition¶

has_diagonalizing_gates¶

has_generator¶

has_matrix¶

has_sparse_matrix = True¶

hash¶

hyperparameters¶

Dictionary of non-trainable variables that this operation depends on.

Type: dict

id¶: Custom string to label a specific operator instance.

is_hermitian¶

name¶: String for the name of the operator.

ndim_params¶

num_params¶

num_wires¶: Number of wires the operator acts on.

parameters¶: Trainable parameters that the operator depends on.

pauli_rep¶: A PauliSentence representation of the Operator, or None if it doesn’t have one.

target_wires¶: The wires of the target operator.

wires¶

work_wires¶: Additional wires that can be used in the decomposition. Not modified by the operation.

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).
`decomposition`()	Representation of the operator as a product of other operators.
`diagonalizing_gates`()	Sequence of gates that diagonalize the operator in the computational basis.
`eigvals`()	Eigenvalues of the operator in the computational basis.
`generator`()	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.
`sparse_matrix`([wire_order, format])	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)¶

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 attribute
wires (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 attribute
wires (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.

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(*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

Operator.matrix() and qml.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()[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

compute_decomposition().

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

compute_diagonalizing_gates().

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

compute_eigvals()

Returns: eigenvalues
Return type: tensor_like

generator()[source]¶

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 * Y(0) + Z(0) @ X(1)

The generator may also be provided in the form of a dense or sparse Hamiltonian (using Hamiltonian and SparseHamiltonian 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 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(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 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)[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: Operator

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

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)[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'>)¶: Append the operator to the Operator queue.

simplify()[source]¶

Reduce the depth of nested operators to the minimum.

Returns: simplified operator
Return type: Operator

sparse_matrix(wire_order=None, format='csr')[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

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]]

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