Channel Capacity¶

arxiv-link Capacities of Quantum Channels and How to Find Them

In [1]:

import numpy as np
import torch
import matplotlib.pyplot as plt

try:
    import numqi
except ImportError:
    %pip install numqi
    import numqi

import numpy as np import torch import matplotlib.pyplot as plt try: import numqi except ImportError: %pip install numqi import numqi

In [2]:

noise_rate_list = np.linspace(0, 1, 20)
hf_channel_list = [
    numqi.channel.hf_amplitude_damping_kraus_op,
    numqi.channel.hf_depolarizing_kraus_op,
    numqi.channel.hf_dephasing_kraus_op,
]

loss_list = []
kwargs = dict(theta0='uniform', num_repeat=3, tol=1e-10, print_every_round=0)
model = numqi.channel.ChannelCapacity1InfModel(2, num_state=2)
for hf_channel in hf_channel_list:
    for noise_rate in noise_rate_list:
        model.set_channel_kraus_op(hf_channel(noise_rate))
        loss_list.append(-numqi.optimize.minimize(model, **kwargs).fun)
loss_list = np.array(loss_list).reshape(len(hf_channel_list), -1)

noise_rate_list = np.linspace(0, 1, 20) hf_channel_list = [ numqi.channel.hf_amplitude_damping_kraus_op, numqi.channel.hf_depolarizing_kraus_op, numqi.channel.hf_dephasing_kraus_op, ] loss_list = [] kwargs = dict(theta0='uniform', num_repeat=3, tol=1e-10, print_every_round=0) model = numqi.channel.ChannelCapacity1InfModel(2, num_state=2) for hf_channel in hf_channel_list: for noise_rate in noise_rate_list: model.set_channel_kraus_op(hf_channel(noise_rate)) loss_list.append(-numqi.optimize.minimize(model, **kwargs).fun) loss_list = np.array(loss_list).reshape(len(hf_channel_list), -1)

In [3]:

fig,ax = plt.subplots()
for ind0,name in enumerate(['amplitude-damping', 'depolarizing', 'phase-damping']):
    ax.plot(noise_rate_list, loss_list[ind0], 'o-', label=name)
ax.set_xlabel('noise rate')
ax.set_ylabel(r'capacity $C_{1,\infty}$')
ax.legend()
ax.grid()
fig.tight_layout()

fig,ax = plt.subplots() for ind0,name in enumerate(['amplitude-damping', 'depolarizing', 'phase-damping']): ax.plot(noise_rate_list, loss_list[ind0], 'o-', label=name) ax.set_xlabel('noise rate') ax.set_ylabel(r'capacity $C_{1,\infty}$') ax.legend() ax.grid() fig.tight_layout()