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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-polynomially-controlled Pauli rotations.\"\"\"","","from __future__ import annotations","from typing import List, Optional","import numpy as np","","from qiskit.circuit import QuantumRegister, AncillaRegister, QuantumCircuit","from qiskit.circuit.exceptions import CircuitError","","from .functional_pauli_rotations import FunctionalPauliRotations","from .polynomial_pauli_rotations import PolynomialPauliRotations","from .integer_comparator import IntegerComparator","","","class PiecewisePolynomialPauliRotations(FunctionalPauliRotations):"," r\"\"\"Piecewise-polynomially-controlled Pauli rotations.",""," This class implements a piecewise polynomial (not necessarily continuous) function,"," :math:`f(x)`, on qubit amplitudes, which is defined through breakpoints and coefficients as"," follows."," Suppose the breakpoints :math:`(x_0, ..., x_J)` are a subset of :math:`[0, 2^n-1]`, where"," :math:`n` is the number of state qubits. Further on, denote the corresponding coefficients by"," :math:`[a_{j,1},...,a_{j,d}]`, where :math:`d` is the highest degree among all polynomials.",""," Then :math:`f(x)` is defined as:",""," .. math::",""," f(x) = \\begin{cases}"," 0, x < x_0 \\\\"," \\sum_{i=0}^{i=d}a_{j,i}/2 x^i, x_j \\leq x < x_{j+1}"," \\end{cases}",""," where if given the same number of breakpoints as polynomials, we implicitly assume"," :math:`x_{J+1} = 2^n`.",""," .. note::",""," Note the :math:`1/2` factor in the coefficients of :math:`f(x)`, this is consistent with"," Qiskit's Pauli rotations.",""," Examples:"," >>> from qiskit import QuantumCircuit"," >>> from qiskit.circuit.library.arithmetic.piecewise_polynomial_pauli_rotations import\\"," ... PiecewisePolynomialPauliRotations"," >>> qubits, breakpoints, coeffs = (2, [0, 2], [[0, -1.2],[-1, 1, 3]])"," >>> poly_r = PiecewisePolynomialPauliRotations(num_state_qubits=qubits,"," ...breakpoints=breakpoints, coeffs=coeffs)"," >>>"," >>> qc = QuantumCircuit(poly_r.num_qubits)"," >>> qc.h(list(range(qubits)));"," >>> qc.append(poly_r.to_instruction(), list(range(qc.num_qubits)));"," >>> qc.draw()"," ┌───┐┌──────────┐"," q_0: ┤ H ├┤0 ├"," ├───┤│ │"," q_1: ┤ H ├┤1 ├"," └───┘│ │"," q_2: ─────┤2 ├"," │ pw_poly │"," q_3: ─────┤3 ├"," │ │"," q_4: ─────┤4 ├"," │ │"," q_5: ─────┤5 ├"," └──────────┘",""," References:"," [1]: Haener, T., Roetteler, M., & Svore, K. M. (2018)."," Optimizing Quantum Circuits for Arithmetic."," `arXiv:1805.12445 `_",""," [2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2022)."," Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation."," `ACM Transactions on Quantum Computing 3, 1, Article 2 `_"," \"\"\"",""," def __init__("," self,"," num_state_qubits: Optional[int] = None,"," breakpoints: Optional[List[int]] = None,"," coeffs: Optional[List[List[float]]] = None,"," basis: str = \"Y\","," name: str = \"pw_poly\","," ) -> None:"," \"\"\""," Args:"," num_state_qubits: The number of qubits representing the state."," breakpoints: The breakpoints to define the piecewise-linear function."," Defaults to ``[0]``."," coeffs: The coefficients of the polynomials for different segments of the"," piecewise-linear function. ``coeffs[j][i]`` is the coefficient of the i-th power of x"," for the j-th polynomial."," Defaults to linear: ``[[1]]``."," basis: The type of Pauli rotation (``'X'``, ``'Y'``, ``'Z'``)."," name: The name of the circuit."," \"\"\""," # store parameters"," self._breakpoints = breakpoints if breakpoints is not None else [0]"," self._coeffs = coeffs if coeffs is not None else [[1]]",""," # store a list of coefficients as homogeneous polynomials adding 0's where necessary"," self._hom_coeffs = []"," self._degree = len(max(self._coeffs, key=len)) - 1"," for poly in self._coeffs:"," self._hom_coeffs.append(poly + [0] * (self._degree + 1 - len(poly)))",""," super().__init__(num_state_qubits=num_state_qubits, basis=basis, name=name)",""," @property"," def breakpoints(self) -> List[int]:"," \"\"\"The breakpoints of the piecewise polynomial function.",""," The function is polynomial in the intervals ``[point_i, point_{i+1}]`` where the last"," point implicitly is ``2**(num_state_qubits + 1)``.",""," Returns:"," The list of breakpoints."," \"\"\""," if ("," self.num_state_qubits is not None"," and len(self._breakpoints) == len(self.coeffs)"," and self._breakpoints[-1] < 2**self.num_state_qubits"," ):"," return self._breakpoints + [2**self.num_state_qubits]",""," return self._breakpoints",""," @breakpoints.setter"," def breakpoints(self, breakpoints: List[int]) -> None:"," \"\"\"Set the breakpoints.",""," Args:"," breakpoints: The new breakpoints."," \"\"\""," self._invalidate()"," self._breakpoints = breakpoints",""," if self.num_state_qubits and breakpoints:"," self._reset_registers(self.num_state_qubits)",""," @property"," def coeffs(self) -> List[List[float]]:"," \"\"\"The coefficients of the polynomials.",""," Returns:"," The polynomial coefficients per interval as nested lists."," \"\"\""," return self._coeffs",""," @coeffs.setter"," def coeffs(self, coeffs: List[List[float]]) -> None:"," \"\"\"Set the polynomials.",""," Args:"," coeffs: The new polynomials."," \"\"\""," self._invalidate()"," self._coeffs = coeffs",""," # update the homogeneous polynomials and degree"," self._hom_coeffs = []"," self._degree = len(max(self._coeffs, key=len)) - 1"," for poly in self._coeffs:"," self._hom_coeffs.append(poly + [0] * (self._degree + 1 - len(poly)))",""," if self.num_state_qubits and coeffs:"," self._reset_registers(self.num_state_qubits)",""," @property"," def mapped_coeffs(self) -> List[List[float]]:"," \"\"\"The coefficients mapped to the internal representation, since we only compare"," x>=breakpoint.",""," Returns:"," The mapped coefficients."," \"\"\""," mapped_coeffs = []",""," # First polynomial"," mapped_coeffs.append(self._hom_coeffs[0])"," for i in range(1, len(self._hom_coeffs)):"," mapped_coeffs.append([])"," for j in range(0, self._degree + 1):"," mapped_coeffs[i].append(self._hom_coeffs[i][j] - self._hom_coeffs[i - 1][j])",""," return mapped_coeffs",""," @property"," def contains_zero_breakpoint(self) -> bool | np.bool_:"," \"\"\"Whether 0 is the first breakpoint.",""," Returns:"," True, if 0 is the first breakpoint, otherwise False."," \"\"\""," return np.isclose(0, self.breakpoints[0])",""," def evaluate(self, x: float) -> float:"," \"\"\"Classically evaluate the piecewise polynomial rotation.",""," Args:"," x: Value to be evaluated at.",""," Returns:"," Value of piecewise polynomial function at x."," \"\"\"",""," y = 0"," for i in range(0, len(self.breakpoints)):"," y = y + (x >= self.breakpoints[i]) * (np.poly1d(self.mapped_coeffs[i][::-1])(x))",""," return y",""," def _check_configuration(self, raise_on_failure: bool = True) -> bool:"," \"\"\"Check if the current configuration is valid.\"\"\""," valid = True",""," 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)"," )",""," if len(self.breakpoints) != len(self.coeffs) + 1:"," valid = False"," if raise_on_failure:"," raise ValueError(\"Mismatching number of breakpoints and polynomials.\")",""," return valid",""," def _reset_registers(self, num_state_qubits: Optional[int]) -> None:"," \"\"\"Reset the registers.\"\"\""," self.qregs = []",""," if num_state_qubits:"," qr_state = QuantumRegister(num_state_qubits)"," qr_target = QuantumRegister(1)"," self.qregs = [qr_state, qr_target]",""," # Calculate number of ancilla qubits required"," num_ancillas = num_state_qubits + 1"," if self.contains_zero_breakpoint:"," num_ancillas -= 1"," if num_ancillas > 0:"," qr_ancilla = AncillaRegister(num_ancillas)"," self.add_register(qr_ancilla)",""," def _build(self):"," \"\"\"If not already built, build the circuit.\"\"\""," if self._is_built:"," return",""," super()._build()",""," circuit = QuantumCircuit(*self.qregs, name=self.name)"," qr_state = circuit.qubits[: self.num_state_qubits]"," qr_target = [circuit.qubits[self.num_state_qubits]]"," # Ancilla for the comparator circuit"," qr_ancilla = circuit.qubits[self.num_state_qubits + 1 :]",""," # apply comparators and controlled linear rotations"," for i, point in enumerate(self.breakpoints[:-1]):"," if i == 0 and self.contains_zero_breakpoint:"," # apply rotation"," poly_r = PolynomialPauliRotations("," num_state_qubits=self.num_state_qubits,"," coeffs=self.mapped_coeffs[i],"," basis=self.basis,"," )"," circuit.append(poly_r.to_gate(), qr_state[:] + qr_target)",""," else:"," # apply Comparator"," comp = IntegerComparator(num_state_qubits=self.num_state_qubits, value=point)"," qr_state_full = qr_state[:] + [qr_ancilla[0]] # add compare qubit"," qr_remaining_ancilla = qr_ancilla[1:] # take remaining ancillas",""," circuit.append("," comp.to_gate(), qr_state_full[:] + qr_remaining_ancilla[: comp.num_ancillas]"," )",""," # apply controlled rotation"," poly_r = PolynomialPauliRotations("," num_state_qubits=self.num_state_qubits,"," coeffs=self.mapped_coeffs[i],"," basis=self.basis,"," )"," circuit.append("," poly_r.to_gate().control(), [qr_ancilla[0]] + qr_state[:] + qr_target"," )",""," # uncompute comparator"," circuit.append("," 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