A brief tutorial how to simulate quantum teleportation with QuTip quantum computing library in Python. More detailed explanation available here: http://mareknarozniak.com/2020/03/22/simulating-quantum-teleportation/
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import matplotlib | |
import matplotlib.pyplot as plt | |
import numpy as np | |
import itertools | |
from qutip import basis, tensor, rand_ket, snot, cnot, rx, rz, qeye | |
# from: https://matplotlib.org/stable/gallery/lines_bars_and_markers/barchart.html#sphx-glr-gallery-lines-bars-and-markers-barchart-py | |
def plotTeleportationOutcomes(outcomes, corrs, labels, title, url=None, filename=None): | |
x = np.arange(len(labels)) # the label locations | |
width = 0.35 # the width of the bars | |
fig, ax = plt.subplots(1, 1, constrained_layout=True) | |
rects1 = ax.bar(x - width/2, outcomes, width, label='not corrected') | |
rects2 = ax.bar(x + width/2, corrs, width, label='corrected') | |
# Add some text for labels, title and custom x-axis tick labels, etc. | |
ax.set_ylabel('fidelity') | |
ax.set_title(title) | |
ax.set_xticks(x) | |
ax.set_xticklabels(labels) | |
ax.legend() | |
ax.bar_label(rects1, padding=3) | |
ax.bar_label(rects2, padding=3) | |
if url is not None: | |
ax.text(0, -0.1, url, fontsize=7) | |
fig.tight_layout() | |
if filename is not None: | |
fig.savefig(filename, transparent=True) | |
# create random state | |
psi = rand_ket(2) | |
# initial state | |
psi0 = tensor([psi, basis(2, 0), basis(2, 0)]) | |
# unitary time-evolution for quantum teleportation | |
psi1 = snot(N=3, target=1)*psi0 | |
psi2 = cnot(N=3, control=1, target=2)*psi1 | |
psi3 = cnot(N=3, control=0, target=1)*psi2 | |
psi4 = snot(N=3, target=0)*psi3 | |
# all the possible outcomes of measurements on first two qubits | |
confs = list(itertools.product([0, 1], repeat=2)) | |
# projection operators | |
Ps = [] | |
for m0, m1 in confs: | |
P = tensor([ | |
basis(2, m0).proj(), | |
basis(2, m1).proj(), | |
qeye(2)]) | |
Ps.append(P) | |
# simulate measurement by performing the projection | |
psis_proj = [] | |
for P in Ps: | |
psi_proj = (P*psi4).unit() | |
psis_proj.append(psi_proj) | |
# classical correction operators | |
X = rx(np.pi, N=3, target=2) | |
Z = rz(np.pi, N=3, target=2) | |
# perform classical correction | |
psis_corr = [ | |
psis_proj[0], | |
X*psis_proj[1], | |
Z*psis_proj[2], | |
Z*X*psis_proj[3] | |
] | |
labels = [] | |
outcomes = [] | |
corrected_outcomes = [] | |
# produce reference states for fidelity calculation | |
psis_ref = [] | |
for m0, m1 in confs: | |
psi_ref = tensor([basis(2, m0), basis(2, m1), psi]) | |
psis_ref.append(psi_ref) | |
labels.append(r'$\left \vert {0}{1} \right \rangle$'.format(str(m0), str(m1))) | |
print() | |
print('classically corrected outcomes fidelities') | |
print('{0:2} {1:2} {2:8}'.format('m0', 'm1', 'fidelity')) | |
for conf, psi_corr, psi_ref in zip(confs, psis_corr, psis_ref): | |
fidelity = np.round(np.abs(psi_corr.overlap(psi_ref))**2., 3) | |
m0, m1 = conf | |
print('{0:2} {1:2} {2:8}'.format(m0, m1, fidelity)) | |
corrected_outcomes.append(fidelity) | |
print() | |
print('fidelities without classical correction') | |
print('{0:2} {1:2} {2:8}'.format('m0', 'm1', 'fidelity')) | |
for conf, psi_proj, psi_ref in zip(confs, psis_proj, psis_ref): | |
fidelity = np.round(np.abs(psi_proj.overlap(psi_ref))**2., 3) | |
m0, m1 = conf | |
print('{0:2} {1:2} {2:8}'.format(m0, m1, fidelity)) | |
outcomes.append(fidelity) | |
# plot the results | |
outcomes = [np.round(out, decimals=2) for out in outcomes] | |
corrected_outcomes = [np.round(out, decimals=2) for out in corrected_outcomes] | |
url = 'https://mareknarozniak.com/2020/03/22/simulating-quantum-teleportation/' | |
title = 'Effect of classical correction on fidelities per outcome' | |
filename = 'outcomes.png' | |
plotTeleportationOutcomes(outcomes, corrected_outcomes, labels, title, url=url, filename=filename) |
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