qml.estimator.ops.PauliRot

class PauliRot(pauli_string, precision=None, wires=None)

Bases: ResourceOperator

Resource class for the PauliRot gate.

Parameters:

• pauli_string (str) – a string describing the Pauli operators that define the rotation

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

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

Resources:

When the pauli_string is a single Pauli operator (X, Y, Z, Identity) the cost is the associated single qubit rotation (RX, RY, RZ, GlobalPhase).

The resources come from Section VIII (Figures 3 & 4) of The Bravyi-Kitaev transformation for quantum computation of electronic structure paper, in combination with the following identities:

\[\begin{split}\begin{align} \hat{X} &= \hat{H} \cdot \hat{Z} \cdot \hat{H}, \\ \hat{Y} &= \hat{S} \cdot \hat{H} \cdot \hat{Z} \cdot \hat{H} \cdot \hat{S}^{\dagger}. \end{align}\end{split}\]

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. Additionally, for each X gate in the Pauli word we conjugate by a pair of Hadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of Hadamard and a pair of S gates.

See also

The corresponding PennyLane operation PauliRot.

Example

The resources for this operation are computed using:

>>> import pennylane.estimator as qre
>>> pr = qre.PauliRot(pauli_string="XYZ")
>>> print(qre.estimate(pr))
--- Resources: ---
 Total wires: 3
    algorithmic wires: 3
    allocated wires: 0
         zero state: 0
         any state: 0
 Total gates : 55
  'T': 44,
  'CNOT': 4,
  'Z': 1,
  'S': 2,
  'Hadamard': 4

Attributes

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

resource_keys = {'pauli_string', 'precision'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• pauli_string (str): a string describing the pauli operators that define the rotation

• 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(pauli_string[, precision])	Returns a list of GateCount objects representing the operator's resources.
resource_rep(pauli_string[, 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)

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:

When the pauli_string is a single Pauli operator (X, Y, Z, Identity) the cost is the associated controlled single qubit rotation gate: (CRX, CRY, CRZ, controlled-GlobalPhase).

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 \(2 \times (n - 1)\) CNOT gates where \(n\) is the number of qubits the gate acts on. Additionally, for each X gate in the Pauli word we conjugate by a pair of Hadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of Hadamard and a pair of S gates.

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 pauli 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(pauli_string, precision=None)

Returns a list of GateCount objects representing the operator’s resources.

Parameters:

• pauli_string (str) – a string describing the pauli operators that define the rotation

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

Resources:

When the pauli_string is a single Pauli operator (X, Y, Z, Identity) the cost is the associated single qubit rotation (RX, RY, RZ, GlobalPhase).

The resources come from Section VIII (Figures 3 & 4) of The Bravyi-Kitaev transformation for quantum computation of electronic structure paper, in combination with the following identity:

\[\begin{split}\begin{align} \hat{X} &= \hat{H} \cdot \hat{Z} \cdot \hat{H}, \\ \hat{Y} &= \hat{S} \cdot \hat{H} \cdot \hat{Z} \cdot \hat{H} \cdot \hat{S}^{\dagger}. \end{align}\end{split}\]

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. Additionally, for each X gate in the Pauli word we conjugate by a pair of Hadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of Hadamard and a pair of S gates.

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(pauli_string, precision=None)

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

Parameters:

• pauli_string (str) – a string describing the pauli operators that define the rotation

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

Returns:

CompressedResourceOp:: the operator in a compressed representation

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