Quick Demo

This notebook is a brief domonstration of the usage of CircuitQ for the Transmon as an exemplary circuit.

Please refer to the Tutorial section for more details.

import circuitq as cq

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt

Exemplary Circuit: Transmon

Create circuit

graph = nx.MultiGraph()
graph.add_edge(0,1, element = 'C')
graph.add_edge(0,1, element = 'J')

circuit = cq.CircuitQ(graph)

Symbolic Hamiltonian

circuit.h

$\displaystyle - E_{J010} \cos{\left(\frac{\Phi_{1}}{\Phi_{o}} \right)} + \frac{0.5 q_{1}^{2}}{C_{01}}$

Parameters

circuit.h_parameters

[C_{01}, E_{J010}]

Numerical Hamiltonian

h_num = circuit.get_numerical_hamiltonian(401, grid_length=np.pi*circuit.phi_0)

Diagonalization

eigv, eigs = circuit.get_eigensystem()

Plot Spectrum

circuit.transform_charge_to_flux()
eigs = circuit.estates_in_phi_basis
n_states = 5
state_scaling = 15 * (eigv[n_states-1]-eigv[0]/n_states)
h = 6.62607015e-34
y_scaling = 1/(h *1e9)

def potential(phi):
    return -circuit.c_v["E"]*np.cos(phi/circuit.phi_0)
plt.plot(circuit.flux_list, potential(circuit.flux_list)*y_scaling, lw=0.7)
for n in range(n_states):
    plt.plot(circuit.flux_list,
             (eigv[n] + np.real(eigs[n]*np.conjugate(eigs[n]))*state_scaling)*y_scaling,
             label="Eigenstate " +str(n))
plt.legend()
plt.xticks(np.linspace(-1*np.pi, 1*np.pi, 3)*circuit.phi_0 ,
           [r'$-\pi$',r'$0$',r'$\pi$'])
plt.xlabel(r"$\Phi_1/ \Phi_o$")
plt.ylabel(r"Energy in GHz$\cdot$h")
plt.show()

\(T1\) Times

T1_qp = circuit.get_T1_quasiparticles()
print("Quasiparticles noise contribution T1 = {:e} s".format(T1_qp))

Quasiparticles noise contribution T1 = 3.103361e-03 s

T1_c = circuit.get_T1_dielectric_loss()
print("Charge noise contribution T1 = {:e} s".format(T1_c))

Charge noise contribution T1 = 1.836958e-04 s

print("Total T1 = {:e} s".format( 1/( 1/T1_qp + 1/T1_c)))

Total T1 = 1.734300e-04 s