qml.estimator.ops.S

class S(wires=None)

Bases: ResourceOperator

Resource class for the S-gate.

Parameters:

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

Resources:

The S gate decomposes into two T gates.

See also

The corresponding PennyLane operation S.

Example

The resources for this operation are computed using:

>>> qml.estimator.S.resource_decomp()
[(2 x T)]

Attributes

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

num_wires = 1

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

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()	Returns a list representing the resources of the operator.
resource_rep()	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=None)

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

Parameters:

target_resource_params (dict | None) – A dictionary containing the resource parameters of the target operator.

Resources:

The adjoint of the S gate is equivalent to \(\hat{Z} \cdot \hat{S}\). The resources are defined as one instance of Z-gate, and one instance of S-gate.

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 | None) – A dictionary containing the resource parameters of the target operator.

Resources:

The controlled-S gate decomposition is presented in (Fig. 5) arXiv:1803.04933. Given a single control wire, the cost is therefore two CNOT gates and three T gates. Two additional X 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 auxiliary qubit in a zeroed state, which is reset at the end. In this case the cost increases by two additional MultiControlledX gates, as described in (Lemma 7.11) Barenco et al. arXiv:quant-ph/9503016.

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=None)

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 | None) – A dictionary containing the resource parameters of the target operator.

Resources:

• The S-gate, when raised to a power which is a multiple of four, produces identity.

• The cost of raising to an arbitrary integer power \(z\), when \(z \mod 4\) is equal to one, means one instance of the S-gate.

• The cost of raising to an arbitrary integer power \(z\), when \(z \mod 4\) is equal to two, means one instance of the Z-gate.

• The cost of raising to an arbitrary integer power \(z\), when \(z \mod 4\) is equal to three, means one instance of the Z-gate and one instance of S-gate.

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()

Returns a list representing the resources of the operator. Each object represents a quantum gate and the number of times it occurs in the decomposition.

Resources:

The S-gate decomposes into two T-gates.

classmethod resource_rep()

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

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