qml.estimator.ops.T

class T(wires=None)

Bases: ResourceOperator

Resource class for the T-gate.

Parameters:

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

Resources:

The T gate is treated as a fundamental gate and thus it cannot be decomposed further. Requesting the resources of this gate raises a ResourcesUndefinedError error.

See also

The corresponding PennyLane operation 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 T-gate is equivalent to the T-gate raised to the 7th power. The resources are defined as one Z-gate (\(Z = T^{4}\)), one S-gate (\(S = T^{2}\)) and one T-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 T-gate is equivalent to the PhaseShift gate for some fixed phase. Given a single control wire, the cost is therefore a single instance of ControlledPhaseShift. 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 T gate, when raised to a power which is a multiple of eight, produces identity. Consequently, for any integer power z, the effective quantum operation \(T^{z}\) is equivalent to \(T^{z \pmod 8}\).

The decomposition for \(T^{z}\), where \(z \pmod 8\) is denoted as z’, is as follows:

• If z’ = 0: The operation is equivalent to the Identity gate (\(I\)).

• If z’ = 1: The operation is equivalent to the T-gate (\(T\)).

• If z’ = 2: The operation is equivalent to the S-gate (\(S\)).

• If z’ = 3: The operation is equivalent to a composition of an S-gate and a T-gate (\(S \cdot T\)).

• If z’ = 4 : The operation is equivalent to the Z-gate (\(Z\)).

• If z’ = 5: The operation is equivalent to a composition of a Z-gate and a T-gate (\(Z \cdot T\)).

• If z’ = 6: The operation is equivalent to a composition of a Z-gate and an S-gate (\(Z \cdot S\)).

• If z’ = 7: The operation is equivalent to a composition of a Z-gate, an S-gate and a T-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 T gate is treated as a fundamental gate and thus it cannot be decomposed further. Requesting the resources of this gate raises a ResourcesUndefinedError error.

Raises:

ResourcesUndefinedError – This gate is fundamental, no further decomposition defined.

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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