qml.estimator.ops.CRot

class CRot(precision=None, wires=None)

Bases: ResourceOperator

Resource class for the CRot gate.

Parameters:

• wires (Sequence[int] | None) – the wire the operation acts on

• precision (float | None) – The error threshold for Clifford + T decomposition of the rotation gate. The default value is None which corresponds to using the epsilon stated in the config.

Resources:

The resources are taken from Figure 1b of arXiv:2110.10292. In combination with the following identity:

\[\begin{split}\begin{align} \hat{RZ}(\theta) = \hat{X} \cdot \hat{RZ}(- \theta) \cdot \hat{X}, \\ \hat{RY}(\theta) = \hat{X} \cdot \hat{RY}(- \theta) \cdot \hat{X}. \end{align}\end{split}\]

This identity is applied along with some clever choices for the angle values to combine rotation; the final circuit takes the form:

ctrl: ─────╭●─────────╭●─────────┤
trgt: ──RZ─╰X──RZ──RY─╰X──RY──RZ─┤

See also

The corresponding PennyLane operation CRot.

Example

The resources for this operation are computed using:

>>> qml.estimator.CRot.resource_decomp()
[(2 x CNOT), (3 x RZ), (2 x RY)]

Attributes

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

num_wires = 2

resource_keys = {'precision'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• precision (float | None): the number of qubits the operation is controlled on

Return type:

dict

Methods

adjoint_resource_decomp(target_resource_params)	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(num_ctrl_wires, ...)	Returns a list representing the resources for a controlled version of the operator.
pow_resource_decomp(pow_z, ...)	Returns a list representing the resources for an operator raised to a power.
resource_decomp([precision])	Returns a list representing the resources of the operator.
resource_rep([precision])	Returns a compressed representation containing only the parameters of the operator that are needed to compute the resources.

classmethod adjoint_resource_decomp(target_resource_params)

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

Parameters:

target_resource_params (dict) – A dictionary containing the resource parameters of the target operator.

Resources:

The adjoint of a general rotation flips the sign of the rotation angle, thus the resources of the adjoint operation result are same as the originial operation.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod controlled_resource_decomp(num_ctrl_wires, num_zero_ctrl, target_resource_params)

Returns a list 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_zero_ctrl (int) – the number of control qubits, that are controlled when in the \(|0\rangle\) state

• target_resource_params (dict) – A dictionary containing the resource parameters of the target operator.

Resources:

The resources are expressed using the symbolic Controlled. The resources are computed according to the controlled_resource_decomp() of the base Rot class.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod pow_resource_decomp(pow_z, target_resource_params)

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

Parameters:

• pow_z (int) – the power that the operator is being raised to

• target_resource_params (dict) – A dictionary containing the resource parameters of the target operator.

Resources:

Taking arbitrary powers of a general single qubit rotation produces a sum of rotations. The resources simplify to just one total single qubit rotation.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod resource_decomp(precision=None)

Returns a list representing the resources of the operator.

Parameters:

precision (float | None) – The error threshold for clifford plus T decomposition of the rotation gate. The default value is None which corresponds to using the epsilon stated in the config.

Resources:

The resources are taken from Figure 1b of arXiv:2110.10292. In combination with the following identity:

\[\begin{split}\begin{align} \hat{RZ}(\theta) = \hat{X} \cdot \hat{RZ}(- \theta) \cdot \hat{X}, \\ \hat{RY}(\theta) = \hat{X} \cdot \hat{RY}(- \theta) \cdot \hat{X}. \end{align}\end{split}\]

This identity is applied along with some clever choices for the angle values to combine rotation; the final circuit takes the form:

ctrl: ─────╭●─────────╭●─────────┤
trgt: ──RZ─╰X──RZ──RY─╰X──RY──RZ─┤

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod resource_rep(precision=None)

Returns a compressed representation containing only the parameters of the operator that are needed to compute the resources.

Parameters:

precision (float | None) – The error threshold for the Clifford + T decomposition of this operation.

Returns:

A compressed representation of the operator.

Return type:

CompressedResourceOp

code/api/pennylane.estimator.ops.CRot

 

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