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# PiecewiseChebyshev¶

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

기반 클래스: 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] and see [2] for a more detailed explanation of the circuit construction and how it acts on the qubits.

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

[2]: Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022).

Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation. ACM Transactions on Quantum Computing 3, 1, Article 2

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

• degree (int | None) – the degree of the polynomials. Defaults to 1.

• breakpoints (list[int] | None) – the breakpoints to define the piecewise-linear function. Defaults to the full interval.

• num_state_qubits (int | None) – 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.

breakpoints

The breakpoints for the piecewise approximation.

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}}

clbits

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

data
degree

The degree of the polynomials.

반환

The degree of the polynomials.

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

The function to be approximated.

반환

The function to be approximated.

global_phase

Return the global phase of the circuit in radians.

instances = 315
layout

Return any associated layout information anout the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or PassManager.run() to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.

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_ancillas

Return the number of ancilla qubits.

num_clbits

Return number of classical bits.

num_parameters
num_qubits

Return number of qubits.

num_state_qubits

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

반환

The number of state qubits.

op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

반환

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

예외 발생

AttributeError – When circuit is not scheduled.

parameters
polynomials

The polynomials for the piecewise approximation.

반환

The polynomials for the piecewise approximation.

예외 발생

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

prefix = 'circuit'
qregs: list[QuantumRegister]

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.