# 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
[documentos]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])
[documentos] 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],
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)