# PiecewiseChebyshev¶

class PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')[소스]

기반 클래스: qiskit.circuit.library.blueprintcircuit.BlueprintCircuit

Piecewise Chebyshev approximation to an input function.

For a given function $$f(x)$$ and degree $$d$$, this class implements a piecewise polynomial Chebyshev approximation on $$n$$ qubits to $$f(x)$$ on the given intervals. All the polynomials in the approximation are of degree $$d$$.

The values of the parameters are calculated according to [1].

예제

import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library.arithmetic.piecewise_chebyshev import PiecewiseChebyshev
f_x, degree, breakpoints, num_state_qubits = lambda x: np.arcsin(1 / x), 2, [2, 4], 2
pw_approximation = PiecewiseChebyshev(f_x, degree, breakpoints, num_state_qubits)
pw_approximation._build()
qc = QuantumCircuit(pw_approximation.num_qubits)
qc.h(list(range(num_state_qubits)))
qc.append(pw_approximation.to_instruction(), qc.qubits)
qc.draw(output='mpl')


참조

[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).

Optimizing Quantum Circuits for Arithmetic. arXiv:1805.12445

매개변수
• f_x (Union[float, Callable[[int], float]]) – the function to be approximated. Constant functions should be specified as f_x = constant.

• degree (Optional[int]) – the degree of the polynomials. Defaults to 1.

• breakpoints (Optional[List[int]]) – the breakpoints to define the piecewise-linear function. Defaults to the full interval.

• num_state_qubits (Optional[int]) – number of qubits representing the state.

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

Attributes

ancillas

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

반환 형식

List[AncillaQubit]

breakpoints

The breakpoints for the piecewise approximation.

반환 형식

List[int]

반환

The breakpoints for the piecewise approximation.

calibrations

Return calibration dictionary.

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

{〈gate_name〉: {(qubits, params): schedule}}

반환 형식

dict

clbits

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

반환 형식

List[Clbit]

data
degree

The degree of the polynomials.

반환 형식

int

반환

The degree of the polynomials.

extension_lib = 'include "qelib1.inc";'
f_x

The function to be approximated.

반환 형식

Union[float, Callable[[int], float]]

반환

The function to be approximated.

global_phase

Return the global phase of the circuit in radians.

반환 형식

Union[ParameterExpression, float]

instances = 9

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.

반환 형식

dict

num_ancillas

Return the number of ancilla qubits.

반환 형식

int

num_clbits

Return number of classical bits.

반환 형식

int

num_parameters
반환 형식

int

num_qubits

Return number of qubits.

반환 형식

int

num_state_qubits

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

반환 형식

int

반환

The number of state qubits.

parameters
반환 형식

ParameterView

polynomials

The polynomials for the piecewise approximation.

반환 형식

List[List[float]]

반환

The polynomials for the piecewise approximation.

예외 발생

TypeError – If the input function is not in the correct format.

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.

반환 형식

List[Qubit]