import numpy as np import matplotlib.pyplot as plt import matplotlib from scipy.linalg import expm from pyqcs import State, sample 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 = 0.09 qbits = list(range(nqbits)) 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) 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) 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[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(-0.5j * t * H(nqbits, g)) T = expm(itH) np_state = T.dot(np_zero_state) 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.") 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 + 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()