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  4. qml.labs.resource_estimation.ResourcePauliRot

qml.labs.resource_estimation.ResourcePauliRot

class ResourcePauliRot(pauli_string, precision=None, wires=None)[source]

Bases: ResourceOperator

Resource class for the PauliRot gate.

Parameters:

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

  • precision (float, optional) – error threshold for clifford plus T decomposition of this operation

  • wires (Sequence[int], optional) – 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 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 ResourceRZ gate and a cascade of \(2 * (n - 1)\) ResourceCNOT 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 ResourceHadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of ResourceHadamard and a pair of ResourceS gates.

See also

PauliRot

Example

The resources for this operation are computed using:

>>> pr = plre.ResourcePauliRot(pauli_string="XYZ")
>>> print(plre.estimate(pr, plre.StandardGate\
Set))
--- Resources: ---
Total qubits: 3
Total gates : 11
Qubit breakdown:
 clean qubits: 0, dirty qubits: 0, algorithmic qubits: 3
Gate breakdown:
 {'Hadamard': 4, 'S': 1, 'Adjoint(S)': 1, 'RZ': 1, 'CNOT': 4}

num_wires

resource_keys

resource_params

Returns a dictionary containing the minimal information needed to compute the resources.
num_wires = 1
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 plus T decomposition of this operation

Return type:

dict

adjoint_resource_decomp(pauli_string[, ...])

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

controlled_resource_decomp(...[, precision])

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

dequeue(op_to_remove[, context])

Remove the given resource operator(s) from the Operator queue.

pow_resource_decomp(pow_z, pauli_string[, ...])

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

queue([context])

Append the operator to the Operator queue.

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.

resource_rep_from_op()

Returns a compressed representation directly from the operator

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.
classmethod adjoint_resource_decomp(pauli_string, precision=None, **kwargs)[source]

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

Parameters:

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

  • precision (float, optional) – error threshold for clifford plus T decomposition of this operation

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(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, pauli_string, precision=None, **kwargs)[source]

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

Parameters:

  • ctrl_num_ctrl_wires (int) – the number of qubits the operation is controlled on

  • ctrl_num_ctrl_values (int) – the number of control qubits, that are controlled when in the \(|0\rangle\) state

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

  • precision (float, optional) – error threshold for clifford plus T decomposition of this operation

Resources:

When the pauli_string is a single Pauli operator (X, Y, Z, Identity) the cost is the associated controlled single qubit rotation gate: (ResourceCRX, ResourceCRY, ResourceCRZ, controlled-ResourceGlobalPhase).

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 \(2 * (n - 1)\) ResourceCNOT 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 ResourceHadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of ResourceHadamard and a pair of ResourceS 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]

static dequeue(op_to_remove, context=<class 'pennylane.queuing.QueuingManager'>)

Remove the given resource operator(s) from the Operator queue.

classmethod pow_resource_decomp(pow_z, pauli_string, precision=None, **kwargs)[source]

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

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

  • precision (float, optional) – error threshold for clifford plus T decomposition of this operation

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]

queue(context=<class 'pennylane.queuing.QueuingManager'>)

Append the operator to the Operator queue.

classmethod resource_decomp(pauli_string, precision=None, **kwargs)[source]

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, optional) – error threshold for clifford plus 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 ResourceRZ gate and a cascade of \(2 * (n - 1)\) ResourceCNOT 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 ResourceHadamard gates, and for each Y gate in the Pauli word we conjugate by a pair of ResourceHadamard and a pair of ResourceS 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)[source]

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, optional) – error threshold for clifford plus T decomposition of this operation

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

resource_rep_from_op()

Returns a compressed representation directly from the operator

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.

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