qml.estimator.templates.PhaseGradient

class PhaseGradient(num_wires=None, wires=None)

Bases: ResourceOperator

Resource class for the PhaseGradient gate.

This operation prepares the phase gradient state \(\frac{1}{\sqrt{2^b}} \cdot \sum_{k=0}^{2^b - 1} e^{-i2\pi \frac{k}{2^b}}\ket{k}\), where \(b\) is the number of qubits. The equation is taken from page 4 of C. Gidney, Quantum 2, 74, (2018).

Parameters:

• num_wires (int | None) – the number of wires to prepare in the phase gradient state

• wires (Sequence[int], None) – the wires the operation acts on

Resources:

The phase gradient state is defined as an equal superposition of phase shifts where each shift is progressively more precise. This is achieved by applying Hadamard gates to each qubit and then applying Z-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:

>>> import pennylane.estimator as qre
>>> phase_grad = qre.PhaseGradient(num_wires=5)
>>> gate_set={"Z", "S", "T", "RZ", "Hadamard"}
>>> print(qre.estimate(phase_grad, gate_set))
--- Resources: ---
Total wires: 5
    algorithmic wires: 5
    allocated wires: 0
    zero state: 0
    any state: 0
Total gates : 10
'RZ': 2,
'T': 1,
'Z': 1,
'S': 1,
'Hadamard': 5

Attributes

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

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

resource_decomp(num_wires)	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.

classmethod resource_decomp(num_wires)

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 phase shifts where each shift is progressively more precise. This is achieved by applying Hadamard gates to each qubit and then applying Z-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

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