Source code for qutip.qip.algorithms.qft

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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