# Quellcode fÃ¼r qiskit.circuit.library.arithmetic.piecewise_linear_pauli_rotations

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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

[Doku]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])

[Doku]    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]

if len(self.breakpoints) > 1:
num_ancillas = num_state_qubits
qr_ancilla = AncillaRegister(num_ancillas)

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],
offset=self.mapped_offsets[i],
basis=self.basis,
)
circuit.append(lin_r.to_gate().control(), qr_compare[:] + qr_state[:] + qr_target)

# uncompute comparator
circuit.append(comp.to_gate().inverse(), qr[:] + qr_helper[: comp.num_ancillas])

self.append(circuit.to_gate(), self.qubits)