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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2020.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"Piecewise polynomial Chebyshev approximation to a given f(x).\"\"\"","","from __future__ import annotations","from typing import Callable","import numpy as np","from numpy.polynomial.chebyshev import Chebyshev","","from qiskit.circuit import QuantumRegister, AncillaRegister","from qiskit.circuit.library.blueprintcircuit import BlueprintCircuit","from qiskit.circuit.exceptions import CircuitError","","from .piecewise_polynomial_pauli_rotations import PiecewisePolynomialPauliRotations","","","class PiecewiseChebyshev(BlueprintCircuit):"," r\"\"\"Piecewise Chebyshev approximation to an input function.",""," For a given function :math:`f(x)` and degree :math:`d`, this class implements a piecewise"," polynomial Chebyshev approximation on :math:`n` qubits to :math:`f(x)` on the given intervals."," All the polynomials in the approximation are of degree :math:`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:",""," .. plot::"," :include-source:",""," 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 `_"," \"\"\"",""," def __init__("," self,"," f_x: float | Callable[[int], float],"," degree: int | None = None,"," breakpoints: list[int] | None = None,"," num_state_qubits: int | None = None,"," name: str = \"pw_cheb\","," ) -> None:"," r\"\"\""," Args:"," f_x: the function to be approximated. Constant functions should be specified"," as f_x = constant."," degree: the degree of the polynomials."," Defaults to ``1``."," breakpoints: the breakpoints to define the piecewise-linear function."," Defaults to the full interval."," num_state_qubits: number of qubits representing the state."," name: The name of the circuit object."," \"\"\""," super().__init__(name=name)",""," # define internal parameters"," self._num_state_qubits = None",""," # Store parameters"," self._f_x = f_x"," self._degree = degree if degree is not None else 1"," self._breakpoints = breakpoints if breakpoints is not None else [0]",""," self._polynomials: list[list[float]] | None = None",""," self.num_state_qubits = num_state_qubits",""," def _check_configuration(self, raise_on_failure: bool = True) -> bool:"," \"\"\"Check if the current configuration is valid.\"\"\""," valid = True",""," if self._f_x is None:"," valid = False"," if raise_on_failure:"," raise AttributeError(\"The function to be approximated has not been set.\")",""," if self._degree is None:"," valid = False"," if raise_on_failure:"," raise AttributeError(\"The degree of the polynomials has not been set.\")",""," if self._breakpoints is None:"," valid = False"," if raise_on_failure:"," raise AttributeError(\"The breakpoints have not been set.\")",""," if self.num_state_qubits is None:"," valid = False"," if raise_on_failure:"," raise AttributeError(\"The number of qubits has not been set.\")",""," if self.num_qubits < self.num_state_qubits + 1:"," valid = False"," if raise_on_failure:"," raise CircuitError("," \"Not enough qubits in the circuit, need at least \""," \"{}.\".format(self.num_state_qubits + 1)"," )",""," return valid",""," @property"," def f_x(self) -> float | Callable[[int], float]:"," \"\"\"The function to be approximated.",""," Returns:"," The function to be approximated."," \"\"\""," return self._f_x",""," @f_x.setter"," def f_x(self, f_x: float | Callable[[int], float] | None) -> None:"," \"\"\"Set the function to be approximated.",""," Note that this may change the underlying quantum register, if the number of state qubits"," changes.",""," Args:"," f_x: The new function to be approximated."," \"\"\""," if self._f_x is None or f_x != self._f_x:"," self._invalidate()"," self._f_x = f_x",""," self._reset_registers(self.num_state_qubits)",""," @property"," def degree(self) -> int:"," \"\"\"The degree of the polynomials.",""," Returns:"," The degree of the polynomials."," \"\"\""," return self._degree",""," @degree.setter"," def degree(self, degree: int | None) -> None:"," \"\"\"Set the error tolerance.",""," Note that this may change the underlying quantum register, if the number of state qubits"," changes.",""," Args:"," degree: The new degree."," \"\"\""," if self._degree is None or degree != self._degree:"," self._invalidate()"," self._degree = degree",""," self._reset_registers(self.num_state_qubits)",""," @property"," def breakpoints(self) -> list[int]:"," \"\"\"The breakpoints for the piecewise approximation.",""," Returns:"," The breakpoints for the piecewise approximation."," \"\"\""," breakpoints = self._breakpoints",""," # it the state qubits are set ensure that the breakpoints match beginning and end"," if self.num_state_qubits is not None:"," num_states = 2**self.num_state_qubits",""," # If the last breakpoint is < num_states, add the identity polynomial"," if breakpoints[-1] < num_states:"," breakpoints = breakpoints + [num_states]",""," # If the first breakpoint is > 0, add the identity polynomial"," if breakpoints[0] > 0:"," breakpoints = [0] + breakpoints",""," return breakpoints",""," @breakpoints.setter"," def breakpoints(self, breakpoints: list[int] | None) -> None:"," \"\"\"Set the breakpoints for the piecewise approximation.",""," Note that this may change the underlying quantum register, if the number of state qubits"," changes.",""," Args:"," breakpoints: The new breakpoints for the piecewise approximation."," \"\"\""," if self._breakpoints is None or breakpoints != self._breakpoints:"," self._invalidate()"," self._breakpoints = breakpoints if breakpoints is not None else [0]",""," self._reset_registers(self.num_state_qubits)",""," @property"," def polynomials(self) -> list[list[float]]:"," \"\"\"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."," \"\"\""," if self.num_state_qubits is None:"," return [[]]",""," # note this must be the private attribute since we handle missing breakpoints at"," # 0 and 2 ^ num_qubits here (e.g. if the function we approximate is not defined at 0"," # and the user takes that into account we just add an identity)"," breakpoints = self._breakpoints"," # Need to take into account the case in which no breakpoints were provided in first place"," if breakpoints == [0]:"," breakpoints = [0, 2**self.num_state_qubits]",""," num_intervals = len(breakpoints)",""," # Calculate the polynomials"," polynomials = []"," for i in range(0, num_intervals - 1):"," # Calculate the polynomial approximating the function on the current interval"," try:"," # If the function is constant don't call Chebyshev (not necessary and gives errors)"," if isinstance(self.f_x, (float, int)):"," # Append directly to list of polynomials"," polynomials.append([self.f_x])"," else:"," poly = Chebyshev.interpolate("," self.f_x, self.degree, domain=[breakpoints[i], breakpoints[i + 1]]"," )"," # Convert polynomial to the standard basis and rescale it for the rotation gates"," poly = 2 * poly.convert(kind=np.polynomial.Polynomial).coef"," # Convert to list and append"," polynomials.append(poly.tolist())"," except ValueError as err:"," raise TypeError("," \" () missing 1 required positional argument: '\""," + self.f_x.__code__.co_varnames[0]"," + \"'.\""," + \" Constant functions should be specified as 'f_x = constant'.\""," ) from err",""," # If the last breakpoint is < 2 ** num_qubits, add the identity polynomial"," if breakpoints[-1] < 2**self.num_state_qubits:"," polynomials = polynomials + [[2 * np.arcsin(1)]]",""," # If the first breakpoint is > 0, add the identity polynomial"," if breakpoints[0] > 0:"," polynomials = [[2 * np.arcsin(1)]] + polynomials",""," return polynomials",""," @polynomials.setter"," def polynomials(self, polynomials: list[list[float]] | None) -> None:"," \"\"\"Set the polynomials for the piecewise approximation.",""," Note that this may change the underlying quantum register, if the number of state qubits"," changes.",""," Args:"," polynomials: The new breakpoints for the piecewise approximation."," \"\"\""," if self._polynomials is None or polynomials != self._polynomials:"," self._invalidate()"," self._polynomials = polynomials",""," self._reset_registers(self.num_state_qubits)",""," @property"," def num_state_qubits(self) -> int:"," r\"\"\"The number of state qubits representing the state :math:`|x\\rangle`.",""," Returns:"," The number of state qubits."," \"\"\""," return self._num_state_qubits",""," @num_state_qubits.setter"," def num_state_qubits(self, num_state_qubits: int | None) -> None:"," \"\"\"Set the number of state qubits.",""," Note that this may change the underlying quantum register, if the number of state qubits"," changes.",""," Args:"," num_state_qubits: The new number of qubits."," \"\"\""," if self._num_state_qubits is None or num_state_qubits != self._num_state_qubits:"," self._invalidate()"," self._num_state_qubits = num_state_qubits",""," # Set breakpoints if they haven't been set"," if num_state_qubits is not None and self._breakpoints is None:"," self.breakpoints = [0, 2**num_state_qubits]",""," self._reset_registers(num_state_qubits)",""," def _reset_registers(self, num_state_qubits: int | None) -> None:"," \"\"\"Reset the registers.\"\"\""," self.qregs = []",""," if num_state_qubits is not None:"," qr_state = QuantumRegister(num_state_qubits, \"state\")"," qr_target = QuantumRegister(1, \"target\")"," self.qregs = [qr_state, qr_target]",""," num_ancillas = num_state_qubits"," if num_ancillas > 0:"," qr_ancilla = AncillaRegister(num_ancillas)"," self.add_register(qr_ancilla)",""," def _build(self):"," \"\"\"Build the circuit if not already build. The operation is considered successful"," when q_objective is :math:`|1>`\"\"\""," if self._is_built:"," return",""," super()._build()",""," poly_r = PiecewisePolynomialPauliRotations("," self.num_state_qubits, self.breakpoints, self.polynomials, name=self.name"," )",""," # qr_state = self.qubits[: self.num_state_qubits]"," # qr_target = [self.qubits[self.num_state_qubits]]"," # qr_ancillas = self.qubits[self.num_state_qubits + 1 :]",""," # Apply polynomial approximation"," self.append(poly_r.to_gate(), 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