/
exact_reciprocal.py
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/
exact_reciprocal.py
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# This code is part of Qiskit.
#
# (C) Copyright IBM 2019, 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.
"""Exact reciprocal rotation."""
from math import isclose
import numpy as np
from qiskit.circuit import QuantumCircuit, QuantumRegister
from qiskit.circuit.library.generalized_gates import UCRYGate
class ExactReciprocal(QuantumCircuit):
r"""Exact reciprocal
.. math::
|x\rangle |0\rangle \mapsto \cos(1/x)|x\rangle|0\rangle + \sin(1/x)|x\rangle |1\rangle
"""
def __init__(
self, num_state_qubits: int, scaling: float, neg_vals: bool = False, name: str = "1/x"
) -> None:
r"""
Args:
num_state_qubits: The number of qubits representing the value to invert.
scaling: Scaling factor :math:`s` of the reciprocal function, i.e. to compute
:math:`s / x`.
neg_vals: Whether :math:`x` might represent negative values. In this case the first
qubit is the sign, with :math:`|1\rangle` for negative and :math:`|0\rangle` for
positive. For the negative case it is assumed that the remaining string represents
:math:`1 - x`. This is because :math:`e^{-2 \pi i x} = e^{2 \pi i (1 - x)}` for
:math:`x \in [0,1)`.
name: The name of the object.
.. note::
It is assumed that the binary string :math:`x` represents a number < 1.
"""
qr_state = QuantumRegister(num_state_qubits, "state")
qr_flag = QuantumRegister(1, "flag")
circuit = QuantumCircuit(qr_state, qr_flag, name=name)
angles = [0.0]
nl = 2 ** (num_state_qubits - 1) if neg_vals else 2**num_state_qubits
# Angles to rotate by scaling / x, where x = i / nl
for i in range(1, nl):
if isclose(scaling * nl / i, 1, abs_tol=1e-5):
angles.append(np.pi)
elif scaling * nl / i < 1:
angles.append(2 * np.arcsin(scaling * nl / i))
else:
angles.append(0.0)
circuit.compose(
UCRYGate(angles), [qr_flag[0]] + qr_state[: len(qr_state) - neg_vals], inplace=True
)
if neg_vals:
circuit.compose(
UCRYGate([-theta for theta in angles]).control(),
[qr_state[-1]] + [qr_flag[0]] + qr_state[:-1],
inplace=True,
)
angles_neg = [0.0]
for i in range(1, nl):
if isclose(scaling * (-1) / (1 - i / nl), -1, abs_tol=1e-5):
angles_neg.append(-np.pi)
elif np.abs(scaling * (-1) / (1 - i / nl)) < 1:
angles_neg.append(2 * np.arcsin(scaling * (-1) / (1 - i / nl)))
else:
angles_neg.append(0.0)
circuit.compose(
UCRYGate(angles_neg).control(),
[qr_state[-1]] + [qr_flag[0]] + qr_state[:-1],
inplace=True,
)
super().__init__(*circuit.qregs, name=name)
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)