qml.estimator.ops.MultiRZ

class MultiRZ(num_wires=None, precision=None, wires=None)

Bases: ResourceOperator

Resource class for the MultiRZ gate.

Parameters:

• num_wires (int | None) – the number of wires the operation acts upon

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

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

Resources:

The resources come from Section VIII (Figure 3) of The Bravyi-Kitaev transformation for quantum computation of electronic structure paper.

Specifically, the resources are given by one RZ gate and a cascade of \(2 \times (n - 1)\) CNOT gates where \(n\) is the number of qubits the gate acts on.

See also

The corresponding PennyLane operation MultiRZ.

Example

The resources for this operation are computed using:

>>> import pennylane.estimator as qre
>>> multi_rz = qre.MultiRZ(num_wires=3)
>>> gate_set = {"CNOT", "RZ"}
>>>
>>> print(qml.estimator.estimate(multi_rz, gate_set))
--- Resources: ---
 Total wires: 3
    algorithmic wires: 3
    allocated wires: 0
         zero state: 0
         any state: 0
 Total gates : 5
  'RZ': 1,
  'CNOT': 4

Attributes

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

resource_keys = {'num_wires', 'precision'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• num_wires (int): the number of qubits the operation acts upon

• precision (float): error threshold for Clifford + T decomposition of this operation

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(num_wires[, precision])	Returns a list representing the resources for a controlled version of the operator.
resource_rep(num_wires[, precision])	Returns a compressed representation containing only the parameters of the Operator that are needed to compute a resource estimation.

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 this operator just changes the sign of the phase, thus the resources of the adjoint operation results in the original 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=None)

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 derived from the following identity. If an operation \(\hat{A}\) can be expressed as \(\hat{A} \ = \ \hat{U} \cdot \hat{B} \cdot \hat{U}^{\dagger}\) then the controlled operation \(C\hat{A}\) can be expressed as:

\[C\hat{A} \ = \ \hat{U} \cdot C\hat{B} \cdot \hat{U}^{\dagger}\]

Specifically, the resources are one multi-controlled RZ-gate and a cascade of \(2 * (n - 1)\) CNOT gates where \(n\) is the number of qubits the gate acts on.

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 rotation produces a sum of rotations. The resources simplify to just one total multi-RZ 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(num_wires, precision=None)

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

Parameters:

• num_wires (int) – the number of qubits the operation acts upon

• precision (float) – error threshold for Clifford + T decomposition of this operation

Resources:

The resources come from Section VIII (Figure 3) of The Bravyi-Kitaev transformation for quantum computation of electronic structure paper.

Specifically, the resources are given by one RZ gate and a cascade of \(2 \times (n - 1)\) CNOT gates where \(n\) is the number of qubits the gate acts on.

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(num_wires, precision=None)

Returns a compressed representation containing only the parameters of the Operator that are needed to compute a resource estimation.

Parameters:

• num_wires (int) – the number of qubits the operation acts upon

• precision (float) – error threshold for Clifford + T decomposition of this operation

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

code/api/pennylane.estimator.ops.MultiRZ

 

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