Quantum process or state tomography of three-qubit gate which generate the GHZ-stae

[hamids...@gmail.com]

Hello,

 I have a question about  Quantum process tomography of three-qubit gate which generates the GHZ-state and its estimated fidelity. My question is "How can i measure the three-qubit entanglement gate via quantum process tomography and its fidelity".

sincerely,

H Sakhouf

[Simon Cross]

Hi Sakhouf,

QuTiP has a guide for this:
https://qutip.org/docs/latest/guide/guide-visualization.html#quantum-process-tomography.
I would recommend starting there.

For your particular case, one could write something like:

""" GHZ tomography """

import matplotlib.pyplot as plt

from qutip import tensor
from qutip import spre, spost, qeye, sigmax, sigmay, sigmaz
from qutip.qip.operations import hadamard_transform, cnot
from qutip.tomography import qpt, qpt_plot_combined

op_basis = [[qeye(2), sigmax(), sigmay(), sigmaz()]] * 3
op_labels = [["i", "x", "y", "z"]] * 3

# plot chi for identity operation for fun and education:

U = qeye([2] * 3)
U_rho = spre(U) * spost(U.dag())

chi = qpt(U_rho, op_basis)
fig, ax = qpt_plot_combined(chi, op_labels)
ax.set_title("chi: Identity")
plt.show()

# plot chi for GHZ circuit [H(0), CNOT(0, 1), CNOT(1, 2)]:

H0 = tensor(hadamard_transform(), qeye(2), qeye(2))
CNOT01 = tensor(cnot(), qeye(2))
CNOT02 = tensor(qeye(2), cnot())

U = CNOT02 * CNOT01 * H0
U_rho = spre(U) * spost(U.dag())

chi = qpt(U_rho, op_basis)
fig, ax = qpt_plot_combined(chi, op_labels)
ax.set_title("chi: GHZ circuit")
plt.show()

# EOF

There are certainly nicer ways to construct the GHZ circuit in QuTiP
using https://qutip.org/docs/latest/guide/qip/qip-basics.html#quantum-circuit,
but I thought it would be instructive to use low-level gate
construction here.

Regards,
Simon

[Hamid Sakhouf]

Hi Simon,

I would like to thank you for your reply, for my case, i want to measure the quantum process and state tomography also its estimated fidelity based on the quantum gate which directly generates the GHZ-state.

Thank you 

Regards,

Sakhouf

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09/11/21, 14:18:57

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