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some work on the presentation

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Daniel Knüttel
2020-02-28 16:09:51 +01:00
parent 7b633f0b62
commit a682dd7f5c
2 changed files with 422 additions and 34 deletions
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presentation/spin_chain/time_evolution.py
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@@ -1,64 +1,87 @@
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
import matplotlib
from scipy.linalg import expm
from pyqcs import State, sample
nqbits = 2
g = 0.20
N = 50
from transfer_matrix import T_time_slice
from hamiltonian import H
from bootstrap import bootstrap
np.random.seed(0xdeadbeef)
matplotlib.rcParams.update(
{'errorbar.capsize': 2
, 'figure.figsize': (16, 9)}
)
nqbits = 6
g = 3
N_trot = 80
t_stop = 9
delta_t = 0.05
delta_t = 0.09
qbits = list(range(nqbits))
n_sample = 400
n_sample = 2200
measure = 0b10
measure_coefficient_mask = [False if (i & measure) else True for i in range(2**nqbits)]
results_qc = []
results_np = []
errors_sampling = []
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
T_dt = T_time_slice(qbits, t, g, N_trot)
for _ in range(N_trot):
state = T_dt * state
#result = sample(state, measure, n_sample)
result = sample(state, measure, n_sample)
results_qc.append(result[0] / n_sample)
#results_qc.append(result[0] / n_sample)
errors_sampling.append(bootstrap(result[0], n_sample, n_sample // 4, n_sample // 10, np.average))
amplitude = np.sqrt(np.sum(np.abs(state._qm_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))
results_qc.append(amplitude)
#amplitude = np.sqrt(np.sum(np.abs(state._qm_state[measure_coefficient_mask])**2))
#results_qc.append(amplitude)
# Simulation using matrices
np_zero_state = np.zeros(2**nqbits)
np_zero_state[0] = 1
itH = np.matrix(-1j * t * H(nqbits, g))
itH = np.matrix(-0.5j * t * H(nqbits, g))
T = expm(itH)
np_state = T.dot(np_zero_state)
amplitude = np.sqrt(np.sum(np.abs(np_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))
amplitude = (np.sum(np.abs(np_state[measure_coefficient_mask])**2))
results_np.append(amplitude)
print(f"simulating... {int(t/t_stop*100)} % ", end="\r")
print()
print("done.")
errors_trotter = np.arange(0, t_stop, delta_t)**2 / N**2
results_qc = np.array(results_qc)
errors_trotter = (np.arange(0, t_stop, delta_t) * g)**2 / N_trot**2
errors_sampling = np.array(errors_sampling)
h0 = plt.errorbar(np.arange(0, t_stop, delta_t), results_qc, yerr=errors_trotter, label=f"Quantum computing ({n_sample} samples, {N} trotterization steps)")
h0 = plt.errorbar(np.arange(0, t_stop, delta_t)
, results_qc
, yerr=(errors_trotter + errors_sampling)
, label=f"Quantum computing ({n_sample} samples, {N_trot} trotterization steps)"
, )
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.savefig("time_evo_6spin_g3.png", dpi=400)
plt.show()