qml.labs.resource_estimation.ResourcePhaseGradient

class ResourcePhaseGradient(num_wires, wires=None)

Bases: ResourceOperator

Resource class for the PhaseGradient gate.

This operation prepares the phase gradient state \(\frac{1}{\sqrt{2^b}} \cdot \sum_{k=0}^{2^b - 1} e^{-i2\pi \frac{k}{2^b}}\ket{k}\).

Parameters:

• num_wires (int) – the number of qubits to prepare in the phase gradient state

• wires (Sequence[int], optional) – the wires the operation acts on

Resources:

The phase gradient state is defined as an equal superposition of phaseshifts where each shift is progressively more precise. This is achieved by applying Hadamard gates to each qubit and then applying RZ-rotations to each qubit with progressively smaller rotation angle. The first three rotations can be compiled to a Z-gate, S-gate and a T-gate.

Example

The resources for this operation are computed using:

>>> phase_grad = plre.ResourcePhaseGradient(num_wires=5)
>>> gate_set={"Z", "S", "T", "RZ", "Hadamard"}
>>> print(plre.estimate(phase_grad, gate_set))
--- Resources: ---
Total qubits: 5
Total gates : 10
Qubit breakdown:
 clean qubits: 0, dirty qubits: 0, algorithmic qubits: 5
Gate breakdown:
 {'Hadamard': 5, 'Z': 1, 'S': 1, 'T': 1, 'RZ': 2}

Attributes

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

num_wires = 1

resource_keys = {'num_wires'}

resource_params

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

Returns:

A dictionary containing the resource parameters:

• num_wires (int): the number of qubits to prepare in the phase gradient state

Return type:

dict

Methods

adjoint_resource_decomp(*args, **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, *args, **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(num_wires, **kwargs)	Returns a list representing the resources of the operator.
resource_rep(num_wires)	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(*args, **kwargs)

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

classmethod controlled_resource_decomp(ctrl_num_ctrl_wires, ctrl_num_ctrl_values, *args, **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

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, *args, **kwargs)

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

Parameters:

pow_z (int) – exponent that the operator is being raised to

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

Append the operator to the Operator queue.

classmethod resource_decomp(num_wires, **kwargs)

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

Parameters:

num_wires (int) – the number of qubits to prepare in the phase gradient state

Resources:

The resources are obtained by construction. The phase gradient state is defined as an equal superposition of phaseshifts where each shift is progressively more precise. This is achieved by applying Hadamard gates to each qubit and then applying RZ-rotations to each qubit with progressively smaller rotation angle. The first three rotations can be compiled to a Z-gate, 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_rep(num_wires)

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

Parameters:

num_wires (int) – the number of qubits to prepare in the phase gradient state

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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