# QuTiP example: Quantum Process Tomography¶

J.R. Johansson and P.D. Nation

In [1]:
%matplotlib inline

In [2]:
import numpy as np

In [3]:
from qutip import *

In [4]:
"""
Plot the process tomography matrices for some 1, 2, and 3-qubit qubit gates.
"""
gates = [['C-NOT', cnot()],
['SWAP', swap()],
['$i$SWAP', iswap()],
['$\sqrt{i\mathrm{SWAP}}$', sqrtiswap()],
['S-NOT', snot()],
['$\pi/2$ phase gate', phasegate(np.pi/2)],
['Toffoli', toffoli()],
['Fredkin', fredkin()]]

In [5]:
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 [6]:
plt_qpt_gate(gates[0]);

In [7]:
plt_qpt_gate(gates[1]);

In [8]:
plt_qpt_gate(gates[2]);

In [9]:
plt_qpt_gate(gates[3]);

In [10]:
plt_qpt_gate(gates[4]);

In [11]:
plt_qpt_gate(gates[5]);

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