PiecewiseChebyshev
class qiskit.circuit.library.PiecewiseChebyshev(f_x, degree=None, breakpoints=None, num_state_qubits=None, name='pw_cheb')
Bases: BlueprintCircuit
Piecewise Chebyshev approximation to an input function.
For a given function and degree , this class implements a piecewise polynomial Chebyshev approximation on qubits to on the given intervals. All the polynomials in the approximation are of degree .
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')
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
Default value: 'include "qelib1.inc";'
f_x
The function to be approximated.
Returns
The function to be approximated.
global_phase
Return the global phase of the current circuit scope in radians.
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 250
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 .
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
Default value: 'circuit'
qregs
Type: 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.