90 lines
2.3 KiB
Python
90 lines
2.3 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib
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from scipy.linalg import expm
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from pyqcs import State, sample
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from transfer_matrix import T_time_slice
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from hamiltonian import H
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from bootstrap import bootstrap
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np.random.seed(0xdeadbeef)
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matplotlib.rcParams.update(
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{'errorbar.capsize': 2
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, 'figure.figsize': (16, 9)}
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)
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nqbits = 6
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g = 3
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N_trot = 80
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t_stop = 9
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delta_t = 0.09
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qbits = list(range(nqbits))
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n_sample = 2200
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measure = 0b10
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measure_coefficient_mask = [False if (i & measure) else True for i in range(2**nqbits)]
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results_qc = []
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results_np = []
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errors_sampling = []
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amplitudes_qc = []
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print()
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for t in np.arange(0, t_stop, delta_t):
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# QC simulation
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state = State.new_zero_state(nqbits)
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T_dt = T_time_slice(qbits, t, g, N_trot)
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for _ in range(N_trot):
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state = T_dt * state
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result = sample(state, measure, n_sample)
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results_qc.append(result[0] / n_sample)
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errors_sampling.append(bootstrap(result[0], n_sample, n_sample, n_sample // 2, np.average))
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#amplitude = np.sum(np.abs(state._qm_state[measure_coefficient_mask])**2)
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#amplitudes_qc.append(amplitude)
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# Simulation using matrices
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np_zero_state = np.zeros(2**nqbits)
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np_zero_state[0] = 1
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itH = np.matrix(-0.5j * t * H(nqbits, g))
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T = expm(itH)
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np_state = T.dot(np_zero_state)
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amplitude = (np.sum(np.abs(np_state[measure_coefficient_mask])**2))
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results_np.append(amplitude)
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print(f"simulating... {int(t/t_stop*100)} % ", end="\r")
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print()
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print("done.")
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results_qc = np.array(results_qc)
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errors_trotter = (np.arange(0, t_stop, delta_t) * g)**3 / N_trot**3
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errors_sampling = np.array(errors_sampling)
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h0 = plt.errorbar(np.arange(0, t_stop, delta_t)
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, results_qc
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, yerr=errors_sampling
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, label=f"Quantum computing ({n_sample} samples, {N_trot} trotterization steps)"
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, )
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h1, = plt.plot(np.arange(0, t_stop, delta_t), results_np, label="Classical simulation using explicit transfer matrix")
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#h2, = plt.plot(np.arange(0, t_stop, delta_t), amplitudes_qc, label="QC amplitude")
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plt.xlabel("t")
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plt.ylabel(r"$|0\rangle$ probability amplitude for second spin")
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plt.title(f"{nqbits} site spin chain with g={g} coupling to external field")
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plt.legend(handles=[h0, h1])
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plt.savefig("time_evo_6spin_g3.png", dpi=400)
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plt.show()
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