PiecewiseChebyshev#

class qiskit.circuit.library.PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')[source]#

Bases: 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.

Examples

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')

(Source code)

../_images/qiskit-circuit-library-PiecewiseChebyshev-1.png

References

[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

Parameters:

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.

Returns:: 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.

Returns:: The degree of the polynomials.

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

f_x#

The function to be approximated.

Returns:: The function to be approximated.

global_phase#: Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'#

instances = 321#

layout#

Return any associated layout information about 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.

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_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 \(|x\rangle\).

Returns:: 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.

Returns:: List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises:: AttributeError -- When circuit is not scheduled.

parameters#

polynomials#

The polynomials for the piecewise approximation.

Returns:: The polynomials for the piecewise approximation.
Raises:: 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.