# 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 sum of two qubit registers using QFT."""
import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.library.basis_change import QFT
from .adder import Adder
[docs]class DraperQFTAdder(Adder):
r"""A circuit that uses QFT to perform in-place addition on two qubit registers.
For registers with :math:`n` qubits, the QFT adder can perform addition modulo
:math:`2^n` (with ``kind="fixed"``) or ordinary addition by adding a carry qubits (with
``kind="half"``).
As an example, a non-fixed_point QFT adder circuit that performs addition on two 2-qubit sized
registers is as follows:
.. parsed-literal::
a_0: ─────────■──────■────────────────────────■────────────────
│ │ │
a_1: ─────────┼──────┼────────■──────■────────┼────────────────
┌──────┐ │P(π) │ │ │ │ ┌───────┐
b_0: ┤0 ├─■──────┼────────┼──────┼────────┼───────┤0 ├
│ │ │P(π/2) │P(π) │ │ │ │
b_1: ┤1 qft ├────────■────────■──────┼────────┼───────┤1 iqft ├
│ │ │P(π/2) │P(π/4) │ │
cout_0: ┤2 ├────────────────────────■────────■───────┤2 ├
└──────┘ └───────┘
**References:**
[1] T. G. Draper, Addition on a Quantum Computer, 2000.
`arXiv:quant-ph/0008033 <https://arxiv.org/pdf/quant-ph/0008033.pdf>`_
[2] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017.
`arXiv:1411.5949 <https://arxiv.org/pdf/1411.5949.pdf>`_
[3] Vedral et al., Quantum Networks for Elementary Arithmetic Operations, 1995.
`arXiv:quant-ph/9511018 <https://arxiv.org/pdf/quant-ph/9511018.pdf>`_
"""
def __init__(
self, num_state_qubits: int, kind: str = "fixed", name: str = "DraperQFTAdder"
) -> 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.
kind: The kind of adder, can be ``'half'`` for a half adder or
``'fixed'`` for a fixed-sized adder. A half adder contains a carry-out to represent
the most-significant bit, but the fixed-sized adder doesn't and hence performs
addition modulo ``2 ** num_state_qubits``.
name: The name of the circuit object.
Raises:
ValueError: If ``num_state_qubits`` is lower than 1.
"""
if kind == "full":
raise ValueError("The DraperQFTAdder only supports 'half' and 'fixed' as ``kind``.")
if num_state_qubits < 1:
raise ValueError("The number of qubits must be at least 1.")
super().__init__(num_state_qubits, name=name)
qr_a = QuantumRegister(num_state_qubits, name="a")
qr_b = QuantumRegister(num_state_qubits, name="b")
qr_list = [qr_a, qr_b]
if kind == "half":
qr_z = QuantumRegister(1, name="cout")
qr_list.append(qr_z)
# add registers
self.add_register(*qr_list)
# define register containing the sum and number of qubits for QFT circuit
qr_sum = qr_b[:] if kind == "fixed" else qr_b[:] + qr_z[:]
num_qubits_qft = num_state_qubits if kind == "fixed" else num_state_qubits + 1
circuit = QuantumCircuit(*self.qregs, name=name)
# build QFT adder circuit
circuit.append(QFT(num_qubits_qft, do_swaps=False).to_gate(), qr_sum[:])
for j in range(num_state_qubits):
for k in range(num_state_qubits - j):
lam = np.pi / (2**k)
circuit.cp(lam, qr_a[j], qr_b[j + k])
if kind == "half":
for j in range(num_state_qubits):
lam = np.pi / (2 ** (j + 1))
circuit.cp(lam, qr_a[num_state_qubits - j - 1], qr_z[0])
circuit.append(QFT(num_qubits_qft, do_swaps=False).inverse().to_gate(), qr_sum[:])
self.append(circuit.to_gate(), self.qubits)