PiecewiseChebyshev¶

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

Bases: 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].

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')

../_images/qiskit.circuit.library.PiecewiseChebyshev_0_0.png

References

[1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).: Optimizing Quantum Circuits for Arithmetic. arXiv:1805.12445

Parameters

f_x (Callable[[int], float]) – the function to be approximated.
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.

breakpoints¶

The breakpoints for the piecewise approximation.

Return type: List[int]
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.

Return type: int
Returns: The degree of the polynomials.

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

f_x¶

The function to be approximated.

Return type: Callable[[int], float]
Returns: The function to be approximated.

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_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.

parameters¶

Return type: ParameterView

polynomials¶

The polynomials for the piecewise approximation.

Return type: List[List[float]]
Returns: The polynomials for the piecewise approximation.

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.