qml.labs.resource_estimation.ResourceT¶

class ResourceT(*params, wires=None, id=None)[source]¶

Bases: pennylane.ops.qubit.non_parametric_ops.T, pennylane.labs.resource_estimation.resource_operator.ResourceOperator

Resource class for the T-gate.

Parameters: wires (Sequence[int] or int) – the wire the operation acts on

Resources:: The T-gate is treated as a fundamental gate and thus it cannot be decomposed further. Requesting the resources of this gate raises a ResourcesNotDefined error.

See also

T

Attributes

`arithmetic_depth`	Arithmetic depth of the operator.
`basis`
`batch_size`
`control_wires`	Control wires of the operator.
`grad_method`	Gradient computation method.
`grad_recipe`	Gradient recipe for the parameter-shift method.
`has_adjoint`
`has_decomposition`
`has_diagonalizing_gates`
`has_generator`
`has_matrix`
`has_plxpr_decomposition`
`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.
`parameter_frequencies`	Returns the frequencies for each operator parameter with respect to an expectation value of the form $\langle \psi \| U(\mathbf{p})^\dagger \hat{O} U(\mathbf{p})\|\psi\rangle$ .
`parameters`	Trainable parameters that the operator depends on.
`pauli_rep`	A `PauliSentence` representation of the Operator, or `None` if it doesn't have one.
`resource_keys`
`resource_params`	Returns a dictionary containing the minimal information needed to compute the resources.
`wires`	Wires that the operator acts on.

arithmetic_depth¶: Arithmetic depth of the operator.

basis = 'Z'¶

batch_size = None¶

control_wires¶

Control wires of the operator.

For operations that are not controlled, this is an empty Wires object of length 0.

Returns: The control wires of the operation.
Return type: Wires

grad_method¶

Gradient computation method.

'A': analytic differentiation using the parameter-shift method.
'F': finite difference numerical differentiation.
None: the operation may not be differentiated.

Default is 'F', or None if the Operation has zero parameters.

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 = False¶

has_decomposition = True¶

has_diagonalizing_gates = False¶

has_generator = False¶

has_matrix = True¶

has_plxpr_decomposition = False¶

has_sparse_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.

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 = 0¶

Number of trainable parameters that the operator depends on.

Type: int

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.

pauli_rep¶

resource_keys = {}¶

resource_params¶

Returns a dictionary containing the minimal information needed to compute the resources.

Returns: Empty dictionary. The resources of this operation don’t depend on any additional parameters.
Return type: dict

wires¶

Wires that the operator acts on.

Returns: wires
Return type: Wires

Methods

`adjoint`()	Create an operation that is the adjoint of this one.
`adjoint_resource_decomp`()	Returns a dictionary representing the resources for the adjoint of the operator.
`compute_decomposition`(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`()	Eigenvalues of the operator in the computational basis (static method).
`compute_matrix`()	Representation of the operator as a canonical matrix in the computational basis (static method).
`compute_qfunc_decomposition`(*args, ...)	Experimental method to compute the dynamic decomposition of the operator with program capture enabled.
`compute_sparse_matrix`(*params[, format])	Representation of the operator as a sparse matrix in the computational basis (static method).
`controlled_resource_decomp`(num_ctrl_wires, ...)	Returns a dictionary representing the resources for a controlled version of the operator.
`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.
`exp_resource_decomp`(scalar, num_steps, ...)	Returns a dictionary representing the resources for the exponentiated operator.
`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.
`pow_resource_decomp`(z)	Returns a dictionary representing the resources for an operator raised to a power.
`queue`([context])	Append the operator to the Operator queue.
`resource_rep`()	Returns a compressed representation containing only the parameters of the Operator that are needed to compute a resource estimation.
`resource_rep_from_op`()	Returns a compressed representation directly from the operator
`resources`(args, *kwargs)	Returns a dictionary representing the resources of the operator.
`set_resources`(new_func)	Set a custom resource method.
`simplify`()	Reduce the depth of nested operators to the minimum.
`single_qubit_rot_angles`()	The parameters required to implement a single-qubit gate as an equivalent `Rot` gate, up to a global phase.
`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.
`tracking_name`(args, *kwargs)	Returns a name used to track the operator during resource estimation.
`tracking_name_from_op`()	Returns the tracking name built with the operator's parameters.

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.

Returns: The adjointed operation.

classmethod adjoint_resource_decomp()[source]¶

Returns a dictionary representing the resources for the adjoint of the operator.

Resources:: The adjoint of the T-gate is equivalent to the T-gate raised to the 7th power. The resources are defined as seven instances of the T-gate.

Returns

The keys are the operators and the associated: values are the counts.

Return type

Dict[CompressedResourceOp, int]

static compute_decomposition(wires)¶

Representation of the operator as a product of other operators (static method).

$O = O_1 O_2 \dots O_n.$

See also

decomposition().

Parameters: wires (Any, Wires) – Single wire that the operator acts on.
Returns: decomposition into lower level operations
Return type: list[Operator]

Example:

>>> print(qml.T.compute_decomposition(0))
[PhaseShift(0.7853981633974483, wires=[0])]

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()¶

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

eigvals()

Returns: eigenvalues
Return type: array

Example

>>> print(qml.T.compute_eigvals())
[1.+0.j 0.70710678+0.70710678j]

static compute_matrix()¶

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()

Returns: matrix
Return type: ndarray

Example

>>> print(qml.T.compute_matrix())
[[1.+0.j         0.        +0.j        ]
 [0.+0.j         0.70710678+0.70710678j]]

static compute_qfunc_decomposition(*args, **hyperparameters)¶

Experimental method to compute the dynamic decomposition of the operator with program capture enabled.

When the program capture feature is enabled with qml.capture.enable(), the decomposition of the operator is computed with this method if it is defined. Otherwise, the compute_decomposition() method is used.

The exception to this rule is when the operator is returned from the compute_decomposition() method of another operator, in which case the decomposition is performed with compute_decomposition() (even if this method is defined), and not with this method.

When compute_qfunc_decomposition is defined for an operator, the control flow operations within the method (specifying the decomposition of the operator) are recorded in the JAX representation.

Note

This method is experimental and subject to change.

See also

compute_decomposition().

Parameters

*args (list) – positional arguments passed to the operator, including trainable parameters and wires
**hyperparameters (dict) – non-trainable hyperparameters of the operator, as stored in the hyperparameters attribute

static compute_sparse_matrix(*params, format='csr', **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
format (str) – format of the returned scipy sparse matrix, for example ‘csr’
**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

static controlled_resource_decomp(num_ctrl_wires, num_ctrl_values, num_work_wires)[source]¶

Returns a dictionary representing the resources for a controlled version of the operator.

Parameters

num_ctrl_wires (int) – the number of qubits the operation is controlled on
num_ctrl_values (int) – the number of control qubits, that are controlled when in the $|0\rangle$ state
num_work_wires (int) – the number of additional qubits that can be used for decomposition

Resources:

The T-gate is equivalent to the PhaseShift gate for some fixed phase. Given a single control wire, the cost is therefore a single instance of ResourceControlledPhaseShift. Two additional ResourceX gates are used to flip the control qubit if it is zero-controlled.

In the case where multiple controlled wires are provided, we can collapse the control wires by introducing one ‘clean’ auxilliary qubit (which gets reset at the end). In this case the cost increases by two additional ResourceMultiControlledX gates, as described in (Lemma 7.11) Barenco et al..

Returns

The keys are the operators and the associated: values are the counts.

Return type

Dict[CompressedResourceOp, int]

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

classmethod exp_resource_decomp(scalar, num_steps, *args, **kwargs)¶

Returns a dictionary representing the resources for the exponentiated operator.

Parameters

scalar (complex) – complex coefficient of the operator in the exponent
num_steps (int) – number of trotter steps to use when decomposing the expoentiated operator

Raises

ResourcesNotDefined – no resources implemented by default

Returns

The keys are the operators and the associated: values are the counts.

Return type

Dict[CompressedResourceOp, int]

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

The generator may also be provided in the form of a dense or sparse Hamiltonian (using LinearCombination and SparseHamiltonian respectively).

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(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)¶

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)¶

A list of new operators equal to this one raised to the given power.

Parameters: z (float) – exponent for the operator
Returns: list[Operator]

classmethod pow_resource_decomp(z)[source]¶

Returns a dictionary representing the resources for an operator raised to a power.

Parameters: z (int) – the power that the operator is being raised to

Resources:: The T-gate, when raised to a power which is a multiple of eight, produces identity. The cost of raising to an arbitrary integer power $z$ is given by $z \mod 8$ instances of the T-gate.

Returns

The keys are the operators and the associated: values are the counts.

Return type

Dict[CompressedResourceOp, int]

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

classmethod resource_rep()[source]¶: Returns a compressed representation containing only the parameters of the Operator that are needed to compute a resource estimation.

resource_rep_from_op()¶: Returns a compressed representation directly from the operator

classmethod resources(*args, **kwargs)¶: Returns a dictionary representing the resources of the operator. The keys are the operators and the associated values are the counts.

classmethod set_resources(new_func)¶: Set a custom resource method.

simplify()¶

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, format='csr')¶

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
format (str) – format of the returned scipy sparse matrix, for example ‘csr’

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]]

classmethod tracking_name(*args, **kwargs)¶: Returns a name used to track the operator during resource estimation.

tracking_name_from_op()¶: Returns the tracking name built with the operator’s parameters.

qml.labs.resource_estimation.ResourceT¶

Attributes

Methods

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qml.labs.resource_estimation.ResourceT¶

Attributes

Methods

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