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"""
This module provides the circuit implementation for Quantum Fourier Transform.
"""
import numpy as np
from qutip.qip.operations.gates import snot, cphase, swap
from qutip.qip.circuit import QubitCircuit
from qutip.qobj import Qobj
__all__ = ['qft', 'qft_steps', 'qft_gate_sequence']
[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:
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:
qc.add_gate("SNOT", targets=[0])
else:
for i in range(N):
for j in range(i):
qc.add_gate("CPHASE", targets=[j], controls=[i],
arg_label=r"{\pi/2^{%d}}" % (i - j),
arg_value=np.pi / (2 ** (i - j)))
qc.add_gate("SNOT", targets=[i])
if swapping:
for i in range(N // 2):
qc.add_gate("SWAP", targets=[N - i - 1, i])
return qc