bachelor_thesis/presentation/spin_chain/time_evolution.py

import numpy as np
import matplotlib.pyplot as plt

from pyqcs import State, sample
from transfer_matrix import T_time_slice
from hamiltonian import H

from scipy.linalg import expm

nqbits = 4
g = 0.5
N = 400
t_stop = 9
delta_t = 0.05
qbits = list(range(nqbits))

n_sample = 200
measure = 0b10


results_qc = []
results_np = []
print()
for t in np.arange(0, t_stop, delta_t):
    # QC simulation
    state = State.new_zero_state(nqbits)

    for _ in range(N):
        state = T_time_slice(qbits, t, g, N) * state

    result = sample(state, measure, n_sample)

    results_qc.append(result[0] / n_sample)

    # Simulation using matrices
    np_zero_state = np.zeros(2**nqbits)
    np_zero_state[0] = 1

    T = expm(-1j * t * H(nqbits, g))
    #for Tv in T:
    #    print(np.sum(np.abs(Tv)))
    #    assert np.isclose(np.sum(np.abs(Tv)), 1)
    np_state = T.dot(np_zero_state)
    amplitude = np.sum(np.abs(np_state[[False if (i & measure) else True for i in range(2**nqbits)]]))
    results_np.append(amplitude)

    print(f"simulating... {int(t/t_stop*100)} %  ", end="\r")
print()
print("done.")

h0, = plt.plot(np.arange(0, t_stop, delta_t), results_qc, label=f"Quantum computing {n_sample} samples")
h1, = plt.plot(np.arange(0, t_stop, delta_t), results_np, label="Classical simulation using explicit transfer matrix")
plt.xlabel("t")
plt.ylabel(r"$|0\rangle$ probability amplitude for second spin")
plt.title(f"{nqbits} site spin chain with g={g} coupling to external field")
plt.legend(handles=[h0, h1])

plt.show()