# Source code for qutip.qip.algorithms.qft

# This file is part of QuTiP: Quantum Toolbox in Python.
#
#    Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
#
#    Redistribution and use in source and binary forms, with or without
#    modification, are permitted provided that the following conditions are
#    met:
#
#    1. Redistributions of source code must retain the above copyright notice,
#       this list of conditions and the following disclaimer.
#
#    2. Redistributions in binary form must reproduce the above copyright
#       notice, this list of conditions and the following disclaimer in the
#       documentation and/or other materials provided with the distribution.
#
#    3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
#       of its contributors may be used to endorse or promote products derived
#       from this software without specific prior written permission.
#
#    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
#    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
#    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
#    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
#    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
#    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
#    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
#    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
#    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
import numpy as np
import scipy.sparse as sp
from qutip.qobj import *
from qutip.qip.gates import snot, cphase, swap
from qutip.qip.circuit import QubitCircuit

[docs]def qft(N=1):
"""
Quantum Fourier Transform operator on N qubits.

Parameters
----------
N : int
Number of qubits.

Returns
-------
QFT: qobj
Quantum Fourier transform operator.

"""
if N < 1:
raise ValueError("Minimum value of N can be 1")

N2 = 2 ** N
phase = 2.0j * np.pi / N2
arr = np.arange(N2)
L, M = np.meshgrid(arr, arr)
L = phase * (L * M)
L = np.exp(L)
dims = [[2] * N, [2] * N]
return Qobj(1.0 / np.sqrt(N2) * L, dims=dims)

[docs]def qft_steps(N=1, swapping=True):
"""
Quantum Fourier Transform operator on N qubits returning the individual
steps as unitary matrices operating from left to right.

Parameters
----------
N: int
Number of qubits.
swap: boolean
Flag indicating sequence of swap gates to be applied at the end or not.

Returns
-------
U_step_list: list of qobj
List of Hadamard and controlled rotation gates implementing QFT.

"""
if N < 1:
raise ValueError("Minimum value of N can be 1")

U_step_list = []
if N == 1:
U_step_list.append(snot())
else:
for i in range(N):
for j in range(i):
U_step_list.append(cphase(np.pi / (2 ** (i - j)), N,
control=i, target=j))
U_step_list.append(snot(N, i))
if swapping is True:
for i in range(N // 2):
U_step_list.append(swap(N, [N - i - 1, i]))

return U_step_list

[docs]def qft_gate_sequence(N=1, swapping=True):
"""
Quantum Fourier Transform operator on N qubits returning the gate sequence.

Parameters
----------
N: int
Number of qubits.
swap: boolean
Flag indicating sequence of swap gates to be applied at the end or not.

Returns
-------
qc: instance of QubitCircuit
Gate sequence of Hadamard and controlled rotation gates implementing
QFT.
"""

if N < 1:
raise ValueError("Minimum value of N can be 1")

qc = QubitCircuit(N)
if N == 1: