# Quantum Process Tomography¶

J.R. Johansson and P.D. Nation

In [1]:
import numpy as np
from qutip import (about, qeye, qpt, qpt_plot_combined, sigmax, sigmay, sigmaz,
spost, spre)
from qutip_qip.operations import (cnot, fredkin, iswap, phasegate, snot,
sqrtiswap, swap, toffoli)

%matplotlib inline

In [2]:
"""
Plot the process tomography matrices for some 1, 2, and 3-qubit qubit gates.
"""
gates = [
["C-NOT", cnot()],
["SWAP", swap()],
["$i$SWAP", iswap()],
[r"$\sqrt{i\mathrm{SWAP}}$", sqrtiswap()],
["S-NOT", snot()],
[r"$\pi/2$ phase gate", phasegate(np.pi / 2)],
["Toffoli", toffoli()],
["Fredkin", fredkin()],
]

In [3]:
def plt_qpt_gate(gate, figsize=(8, 6)):

name = gate[0]
U_psi = gate[1]

N = len(U_psi.dims[0])  # number of qubits

# create a superoperator for the density matrix
# transformation rho = U_psi * rho_0 * U_psi.dag()
U_rho = spre(U_psi) * spost(U_psi.dag())

# operator basis for the process tomography
op_basis = [[qeye(2), sigmax(), sigmay(), sigmaz()] for i in range(N)]

# labels for operator basis
op_label = [["$i$", "$x$", "$y$", "$z$"] for i in range(N)]

# calculate the chi matrix
chi = qpt(U_rho, op_basis)

# visualize the chi matrix
fig, ax = qpt_plot_combined(chi, op_label, name, figsize=figsize)

ax.set_title(name)

return fig, ax

In [4]:
plt_qpt_gate(gates[0]);

In [5]:
plt_qpt_gate(gates[1]);

In [6]:
plt_qpt_gate(gates[2]);

In [7]:
plt_qpt_gate(gates[3]);

In [8]:
plt_qpt_gate(gates[4]);

In [9]:
plt_qpt_gate(gates[5]);

In [10]:
fig, ax = plt_qpt_gate(gates[6], figsize=(16, 12))
ax.axis("tight");