# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2021.
#
# 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.
"""Compute the product of two qubit registers using QFT."""
from typing import Optional
import numpy as np
from qiskit.circuit import QuantumRegister, QuantumCircuit
from qiskit.circuit.library.standard_gates import PhaseGate
from qiskit.circuit.library.basis_change import QFT
from .multiplier import Multiplier
[documentos]class RGQFTMultiplier(Multiplier):
r"""A QFT multiplication circuit to store product of two input registers out-of-place.
Multiplication in this circuit is implemented using the procedure of Fig. 3 in [1], where
weighted sum rotations are implemented as given in Fig. 5 in [1]. QFT is used on the output
register and is followed by rotations controlled by input registers. The rotations
transform the state into the product of two input registers in QFT base, which is
reverted from QFT base using inverse QFT.
As an example, a circuit that performs a modular QFT multiplication on two 2-qubit
sized input registers with an output register of 2 qubits, is as follows:
.. parsed-literal::
a_0: βββββββββββββββββββββββββββββββββββββββββ ββββββββ βββββββ βββββββ ββββββββββββββββ
β β β β
a_1: ββββββββββ ββββββββ ββββββββ ββββββββ βββββββΌββββββββΌβββββββΌβββββββΌββββββββββββββββ
β β β β β β β β
b_0: ββββββββββΌββββββββΌββββββββ ββββββββ βββββββΌββββββββΌβββββββ βββββββ ββββββββββββββββ
β β β β β β β β
b_1: ββββββββββ ββββββββ ββββββββΌββββββββΌβββββββ ββββββββ βββββββΌβββββββΌββββββββββββββββ
ββββββββ βP(4Ο) β βP(2Ο) β βP(2Ο) β βP(Ο) β βββββββββ
out_0: β€0 βββ ββββββββΌββββββββ ββββββββΌβββββββ ββββββββΌβββββββ βββββββΌββββββββ€0 β
β qft β βP(2Ο) βP(Ο) βP(Ο) βP(Ο/2) β iqft β
out_1: β€1 βββββββββββ ββββββββββββββββ βββββββββββββββ ββββββββββββββ ββββββββ€1 β
ββββββββ βββββββββ
**References:**
[1] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017.
`arXiv:1411.5949 <https://arxiv.org/pdf/1411.5949.pdf>`_
"""
def __init__(
self,
num_state_qubits: int,
num_result_qubits: Optional[int] = None,
name: str = "RGQFTMultiplier",
) -> None:
r"""
Args:
num_state_qubits: The number of qubits in either input register for
state :math:`|a\rangle` or :math:`|b\rangle`. The two input
registers must have the same number of qubits.
num_result_qubits: The number of result qubits to limit the output to.
If number of result qubits is :math:`n`, multiplication modulo :math:`2^n` is performed
to limit the output to the specified number of qubits. Default
value is ``2 * num_state_qubits`` to represent any possible
result from the multiplication of the two inputs.
name: The name of the circuit object.
"""
super().__init__(num_state_qubits, num_result_qubits, name=name)
# define the registers
qr_a = QuantumRegister(num_state_qubits, name="a")
qr_b = QuantumRegister(num_state_qubits, name="b")
qr_out = QuantumRegister(self.num_result_qubits, name="out")
self.add_register(qr_a, qr_b, qr_out)
# build multiplication circuit
circuit = QuantumCircuit(*self.qregs, name=name)
circuit.append(QFT(self.num_result_qubits, do_swaps=False).to_gate(), qr_out[:])
for j in range(1, num_state_qubits + 1):
for i in range(1, num_state_qubits + 1):
for k in range(1, self.num_result_qubits + 1):
lam = (2 * np.pi) / (2 ** (i + j + k - 2 * num_state_qubits))
circuit.append(
PhaseGate(lam).control(2),
[qr_a[num_state_qubits - j], qr_b[num_state_qubits - i], qr_out[k - 1]],
)
circuit.append(QFT(self.num_result_qubits, do_swaps=False).inverse().to_gate(), qr_out[:])
self.append(circuit.to_gate(), self.qubits)