qml.labs.resource_estimation.ResourceT

class ResourceT(*args, wires=None, **kwargs)

Bases: ResourceOperator

Resource class for the T-gate.

Parameters:

wires (Sequence[int] or int, optional) – 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 ResourcesNotDefined error.

See also

T

Attributes

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

num_wires = 1

resource_keys = {}

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(**kwargs)	Returns a list representing the resources for the adjoint of the operator.
controlled_resource_decomp(...)	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, **kwargs)	Returns a list representing the resources for an operator raised to a power.
queue([context])	Append the operator to the Operator queue.
resource_decomp(**kwargs)	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.
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(**kwargs)

Returns a list representing the resources for the adjoint of the 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(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, **kwargs)

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

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 ResourceControlledPhaseShift. Two additional ResourceX 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 ‘clean’ auxilliary qubit (which gets reset at the end). In this case the cost increases by two additional ResourceMultiControlledX gates, as described in (Lemma 7.11) Barenco et al..

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, **kwargs)

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

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]

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

Append the operator to the Operator queue.

classmethod resource_decomp(**kwargs)

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 ResourcesNotDefined error.

Raises:

ResourcesNotDefined – 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.

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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