absorptive_graph.py

"""If you find the codes in this repository useful, please cite this work as follows:
--- A. Zang, A. Kolar, J. Chung, M. Suchara, T. Zhong and R. Kettimuthu, "Simulation of Entanglement Generation between Absorptive Quantum Memories," 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), Broomfield, CO, USA, 2022, pp. 617-623, doi: 10.1109/QCE53715.2022.00084. 
"""

from json import load
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import matplotlib.ticker as tck
from matplotlib.colors import LightSource


filename = "results/absorptive.json"
data = load(open(filename))

direct_results = data["direct results"]
bs_results = data["bs results"]

# acquire direct detection results
bins = np.zeros(4)
for trial in direct_results:
    bins += np.array(trial["counts"])
bins *= (1 / sum(bins))

# acquire bs results
num = data["num_phase"]
phases = np.linspace(0, 2*np.pi, num=num)
freq_0 = []
freq_1 = []
st_dev_0 = []
st_dev_1 = []
for res in bs_results:
    counts = []
    total = 0
    for trial in res:
        counts.append(trial["counts1"])
        total += trial["total_count1"]
    counts = np.array(counts, dtype=float)
    st_dev = np.std(counts, axis=0)
    # average
    counts = np.sum(counts, axis=0)
    counts *= (1 / total)
    st_dev *= (1 / total)
    freq_0.append(counts[0])
    freq_1.append(counts[1])
    st_dev_0.append(2 * st_dev[0])  # mult. by 2, so have 1 on top and bottom of point
    st_dev_1.append(2 * st_dev[1])

# curve fitting
def sin(x, A, phi, z): return A*np.sin(x + phi) + z
params_0, _ = curve_fit(sin, phases, freq_0)
params_1, _ = curve_fit(sin, phases, freq_1)
vis_0 = abs(params_0[0]) / abs(params_0[2])
vis_1 = abs(params_1[0]) / abs(params_1[2])

# off-diagonal density matrix
vis_total = (vis_0 + vis_1) / 2
off_diag = vis_total * (bins[1] + bins[2]) / 2

# plotting density matrix
# plot the 2-d matrix
plt.rc('font', size=10)
plt.rc('axes', titlesize=18)
plt.rc('axes', labelsize=15)
plt.rc('xtick', labelsize=15)
plt.rc('ytick', labelsize=15)
plt.rc('legend', fontsize=15)

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(projection="3d")
ax.view_init(azim=-30, elev=20)

offset = 3
total = list(bins) + [off_diag, off_diag]
height = np.log10(total) + offset
width = depth = 0.8
x = np.array([0, 1, 2, 3, 1, 2]) - (width/2)
y = np.array([0, 1, 2, 3, 2, 1]) - (width/2)
color = (['tab:blue'] * 4) + (['tab:orange'] * 2)
ls = LightSource(100, 60)
ax.bar3d(x, y, np.zeros(6), width, depth, height,
         color=color, edgecolor='black', shade=True, lightsource=ls)

def log_tick_formatter(val, pos=None): return f"$10^{{{int(val-offset)}}}$"
ax.zaxis.set_major_formatter(tck.FuncFormatter(log_tick_formatter))
ax.zaxis.set_major_locator(tck.MaxNLocator(integer=True))

# ax.set_title(r'Reconstructed $|\tilde{\rho}|$')
ax.set_xticks([0, 1, 2, 3])
ax.set_yticks([0, 1, 2, 3])
ax.set_xticklabels([r'$|00\rangle$', r'$|01\rangle$', r'$|10\rangle$', r'$|11\rangle$'])
ax.set_yticklabels([r'$\langle00|$', r'$\langle01|$', r'$\langle10|$', r'$\langle11|$'])
plt.savefig('density.png', bbox_inches='tight')
plt.show()

# plotting interference
fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot()

ax.errorbar(phases/np.pi, freq_0, yerr=st_dev_0, marker='o', ls='', capsize=5, label=r'$p_{01}$')
ax.errorbar(phases/np.pi, freq_1, yerr=st_dev_1, marker='o', ls='', capsize=5, label=r'$p_{10}$')
ax.plot(phases/np.pi, np.zeros(phases.shape), ls='--', color='gray')
plt.plot(phases/np.pi, sin(phases, *params_0), color='tab:blue', ls='--')
plt.plot(phases/np.pi, sin(phases, *params_1), color='tab:orange', ls='--')

ax.set_title("Photon Interference")
ax.xaxis.set_major_formatter(tck.FormatStrFormatter(r'%g $\pi$'))
ax.xaxis.set_major_locator(tck.MultipleLocator(base=0.5))
ax.set_xlabel("Relative Phase")
ax.set_ylabel("Detection Rate")
ax.legend()
fig.tight_layout()
plt.savefig('interference.png')
plt.show()

# output
print("Detector 1 visibility:", vis_1)
print("Detector 2 visibility:", vis_0)
print("Combined:", vis_total)
print("Off-diagonal:", off_diag)