C贸digo fuente para qiskit.circuit.library.arithmetic.adders.draper_qft_adder

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"""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


[documentos]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: 鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 鈹 鈹 鈹 a_1: 鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹 鈹屸攢鈹鈹鈹鈹鈹鈹 鈹侾(蟺) 鈹 鈹 鈹 鈹 鈹屸攢鈹鈹鈹鈹鈹鈹鈹 b_0: 鈹0 鈹溾攢鈻犫攢鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹0 鈹 鈹 鈹 鈹侾(蟺/2) 鈹侾(蟺) 鈹 鈹 鈹 鈹 b_1: 鈹1 qft 鈹溾攢鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹鈹尖攢鈹鈹鈹鈹鈹鈹鈹1 iqft 鈹 鈹 鈹 鈹侾(蟺/2) 鈹侾(蟺/4) 鈹 鈹 cout_0: 鈹2 鈹溾攢鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹鈻犫攢鈹鈹鈹鈹鈹鈹鈹2 鈹 鈹斺攢鈹鈹鈹鈹鈹鈹 鈹斺攢鈹鈹鈹鈹鈹鈹鈹 **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)