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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-linearly-controlled rotation.\"\"\"","","from __future__ import annotations","import numpy as np","","from qiskit.circuit import QuantumRegister, AncillaRegister, QuantumCircuit","from qiskit.circuit.exceptions import CircuitError","","from .functional_pauli_rotations import FunctionalPauliRotations","from .linear_pauli_rotations import LinearPauliRotations","from .integer_comparator import IntegerComparator","","","class PiecewiseLinearPauliRotations(FunctionalPauliRotations):"," r\"\"\"Piecewise-linearly-controlled Pauli rotations.",""," For a piecewise linear (not necessarily continuous) function :math:`f(x)`, which is defined"," through breakpoints, slopes and offsets 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 slopes and"," offsets by :math:`a_j` and :math:`b_j` respectively."," Then f(x) is defined as:",""," .. math::",""," f(x) = \\begin{cases}"," 0, x < x_0 \\\\"," a_j (x - x_j) + b_j, x_j \\leq x < x_{j+1}"," \\end{cases}",""," where we implicitly assume :math:`x_{J+1} = 2^n`."," \"\"\"",""," def __init__("," self,"," num_state_qubits: int | None = None,"," breakpoints: list[int] | None = None,"," slopes: list[float] | np.ndarray | None = None,"," offsets: list[float] | np.ndarray | None = None,"," basis: str = \"Y\","," name: str = \"pw_lin\","," ) -> None:"," \"\"\"Construct piecewise-linearly-controlled Pauli rotations.",""," Args:"," num_state_qubits: The number of qubits representing the state."," breakpoints: The breakpoints to define the piecewise-linear function."," Defaults to ``[0]``."," slopes: The slopes for different segments of the piecewise-linear function."," Defaults to ``[1]``."," offsets: The offsets for different segments of the piecewise-linear function."," Defaults to ``[0]``."," 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._slopes = slopes if slopes is not None else [1]"," self._offsets = offsets if offsets is not None else [0]",""," super().__init__(num_state_qubits=num_state_qubits, basis=basis, name=name)",""," @property"," def breakpoints(self) -> list[int]:"," \"\"\"The breakpoints of the piecewise linear function.",""," The function is linear in the intervals ``[point_i, point_{i+1}]`` where the last"," point implicitly is ``2**(num_state_qubits + 1)``."," \"\"\""," 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 slopes(self) -> list[float] | np.ndarray:"," \"\"\"The breakpoints of the piecewise linear function.",""," The function is linear in the intervals ``[point_i, point_{i+1}]`` where the last"," point implicitly is ``2**(num_state_qubits + 1)``."," \"\"\""," return self._slopes",""," @slopes.setter"," def slopes(self, slopes: list[float]) -> None:"," \"\"\"Set the slopes.",""," Args:"," slopes: The new slopes."," \"\"\""," self._invalidate()"," self._slopes = slopes",""," @property"," def offsets(self) -> list[float] | np.ndarray:"," \"\"\"The breakpoints of the piecewise linear function.",""," The function is linear in the intervals ``[point_i, point_{i+1}]`` where the last"," point implicitly is ``2**(num_state_qubits + 1)``."," \"\"\""," return self._offsets",""," @offsets.setter"," def offsets(self, offsets: list[float]) -> None:"," \"\"\"Set the offsets.",""," Args:"," offsets: The new offsets."," \"\"\""," self._invalidate()"," self._offsets = offsets",""," @property"," def mapped_slopes(self) -> np.ndarray:"," \"\"\"The slopes mapped to the internal representation.",""," Returns:"," The mapped slopes."," \"\"\""," mapped_slopes = np.zeros_like(self.slopes)"," for i, slope in enumerate(self.slopes):"," mapped_slopes[i] = slope - sum(mapped_slopes[:i])",""," return mapped_slopes",""," @property"," def mapped_offsets(self) -> np.ndarray:"," \"\"\"The offsets mapped to the internal representation.",""," Returns:"," The mapped offsets."," \"\"\""," mapped_offsets = np.zeros_like(self.offsets)"," for i, (offset, slope, point) in enumerate("," zip(self.offsets, self.slopes, self.breakpoints)"," ):"," mapped_offsets[i] = offset - slope * point - sum(mapped_offsets[:i])",""," return mapped_offsets",""," @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 linear rotation.",""," Args:"," x: Value to be evaluated at.",""," Returns:"," Value of piecewise linear function at x."," \"\"\"",""," y = (x >= self.breakpoints[0]) * (x * self.mapped_slopes[0] + self.mapped_offsets[0])"," for i in range(1, len(self.breakpoints)):"," y = y + (x >= self.breakpoints[i]) * ("," x * self.mapped_slopes[i] + self.mapped_offsets[i]"," )",""," 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.slopes) or len(self.breakpoints) != len(self.offsets):"," valid = False"," if raise_on_failure:"," raise ValueError(\"Mismatching sizes of breakpoints, slopes and offsets.\")",""," return valid",""," 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)"," qr_target = QuantumRegister(1)"," self.qregs = [qr_state, qr_target]",""," # add ancillas if required"," if len(self.breakpoints) > 1:"," num_ancillas = num_state_qubits"," 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]]"," qr_ancilla = circuit.ancillas",""," # apply comparators and controlled linear rotations"," for i, point in enumerate(self.breakpoints):"," if i == 0 and self.contains_zero_breakpoint:"," # apply rotation"," lin_r = LinearPauliRotations("," num_state_qubits=self.num_state_qubits,"," slope=self.mapped_slopes[i],"," offset=self.mapped_offsets[i],"," basis=self.basis,"," )"," circuit.append(lin_r.to_gate(), qr_state[:] + qr_target)",""," else:"," qr_compare = [qr_ancilla[0]]"," qr_helper = qr_ancilla[1:]",""," # apply Comparator"," comp = IntegerComparator(num_state_qubits=self.num_state_qubits, value=point)"," qr = qr_state[:] + qr_compare[:] # add ancilla as compare qubit",""," circuit.append(comp.to_gate(), qr[:] + qr_helper[: comp.num_ancillas])",""," # apply controlled rotation"," lin_r = LinearPauliRotations("," num_state_qubits=self.num_state_qubits,"," slope=self.mapped_slopes[i],"," 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