LinearPauliRotations

class LinearPauliRotations(num_state_qubits=None, slope=1, offset=0, basis='Y', name='LinRot')

Bases: qiskit.circuit.library.arithmetic.functional_pauli_rotations.FunctionalPauliRotations

Linearly-controlled X, Y or Z rotation.

For a register of state qubits \(|x\rangle\), a target qubit \(|0\rangle\) and the basis 'Y' this circuit acts as:

    q_0: ─────────────────────────■───────── ... ──────────────────────
                                  │
                                  .
                                  │
q_(n-1): ─────────────────────────┼───────── ... ───────────■──────────
          ┌────────────┐  ┌───────┴───────┐       ┌─────────┴─────────┐
    q_n: ─┤ RY(offset) ├──┤ RY(2^0 slope) ├  ...  ┤ RY(2^(n-1) slope) ├
          └────────────┘  └───────────────┘       └───────────────────┘

This can for example be used to approximate linear functions, with \(a/2 =\) slope and \(b/2 =\) offset and the basis 'Y':

\[|x\rangle |0\rangle \mapsto \cos(ax + b)|x\rangle|0\rangle + \sin(ax + b)|x\rangle |1\rangle\]

Since for small arguments \(\sin(x) \approx x\) this operator can be used to approximate linear functions.

Create a new linear rotation circuit.

Parameters

• num_state_qubits (Optional[int]) – The number of qubits representing the state \(|x\rangle\).

• slope (float) – The slope of the controlled rotation.

• offset (float) – The offset of the controlled rotation.

• basis (str) – The type of Pauli rotation (‘X’, ‘Y’, ‘Z’).

• name (str) – The name of the circuit object.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

basis

The kind of Pauli rotation to be used.

Set the basis to ‘X’, ‘Y’ or ‘Z’ for controlled-X, -Y, or -Z rotations respectively.

Return type

str

Returns

The kind of Pauli rotation used in controlled rotation.

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{‘gate_name’: {(qubits, params): schedule}}

clbits

Returns a list of classical bits in the order that the registers were added.

data

extension_lib = 'include "qelib1.inc";'

global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'

instances = 16

metadata

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

num_ancilla_qubits

The minimum number of ancilla qubits in the circuit.

Return type

int

Returns

The minimal number of ancillas required.

num_ancillas

Return the number of ancilla qubits.

num_clbits

Return number of classical bits.

num_parameters

Return type

int

num_qubits

Return number of qubits.

num_state_qubits

The number of state qubits representing the state \(|x\rangle\).

Return type

int

Returns

The number of state qubits.

offset

The angle of the single qubit offset rotation on the target qubit.

Before applying the controlled rotations, a single rotation of angle offset is applied to the target qubit.

Return type

float

Returns

The offset angle.

parameters

Return type

ParameterView

prefix = 'circuit'

qregs

A list of the quantum registers associated with the circuit.

qubits

Returns a list of quantum bits in the order that the registers were added.

slope

The multiplicative factor in the rotation angle of the controlled rotations.

The rotation angles are slope * 2^0, slope * 2^1, … , slope * 2^(n-1) where n is the number of state qubits.

Return type

float

Returns

The rotation angle common in all controlled rotations.