[PYTHON] Qiskit: Quantum Fourier Transform

Overview

The quantum Fourier transform is an implementation of the discrete Fourier transform on a quantum circuit. I will leave the detailed explanation to reference books and other sites, and here I would like to implement it with Qiskit. It's completely memorial, so don't worry about the details. In the future, I would like to implement other algorithms etc. using this code.

code

python

# coding: utf-8

from qiskit import QuantumRegister, QuantumCircuit, ClassicalRegister
from math import log2, pi
import numpy as np


class QFT:

    def __init__(self, numQubit):
        self.numQubit = numQubit

    def construct_circuit(self, circuit=None, inverse=False):
        if circuit is None:
            circuit = QuantumCircuit(range(self.numQubit))
        if not inverse:
            self._input_initial_state(circuit)
            self._qft(circuit)
            self._swap_registers(circuit)
            return circuit
        elif inverse:
            self._swap_registers(circuit)
            self._qft(circuit, inverse=True)
            self._input_initial_state(circuit, inverse=True)
            return circuit

    def _input_initial_state(self, circuit, inverse=False):
        if not inverse:
            for j in range(self.numQubit):
                circuit.h(j)
                circuit.u1(-pi / float(2 ** j), j)
        elif inverse:
            for j in range(self.numQubit):
                circuit.u1(-pi / float(2 ** j), j)
                circuit.h(j)

    def _qft(self, circuit, inverse=False):
        if not inverse:
            for j in range(self.numQubit):
                circuit.h(j)
                for k in range(j + 1, self.numQubit):
                    circuit.cu1(pi / float(2 ** (k - j)), k, j)
        elif inverse:
            for j in range(self.numQubit).__reversed__():
                for k in range(j + 1, self.numQubit).__reversed__():
                    circuit.cu1(pi / float(2 ** (k - j)), k, j)
                circuit.h(j)
        circuit.barrier()

    def _swap_registers(self, circuit):
        for j in range(int(np.floor(self.numQubit / 2.))):
            circuit.swap(j, self.numQubit - j - 1)

References

[1]Qiskit textbook