CNOT[4, 3] = 1
CNOT[5, 5] = 1
CNOT = DenseOperator(CNOT)
CNOT_4 = CNOT.truncate_to_subspace(comp_sub_sub_space_ind)
def exchange_interaction(amplitude):
return np.exp(amplitude)
def deriv_exchange_interaction(amplitude):
return np.exp(amplitude)
sig_1_z = SIGMA_Z.kron(SIGMA_0).kron(SIGMA_0).kron(SIGMA_0)
sig_2_z = SIGMA_0.kron(SIGMA_Z).kron(SIGMA_0).kron(SIGMA_0)
sig_3_z = SIGMA_0.kron(SIGMA_0).kron(SIGMA_Z).kron(SIGMA_0)
sig_4_z = SIGMA_0.kron(SIGMA_0).kron(SIGMA_0).kron(SIGMA_Z)
h_drift = B12 / 8 * ((-3 * sig_1_z) + sig_2_z + sig_3_z + sig_4_z) \
+ B23 / 4 * ((-1 * sig_1_z) - sig_2_z + sig_3_z + sig_4_z) \
+ B34 / 8 * ((-1 * sig_1_z) - sig_2_z - sig_3_z + (3 * sig_4_z))
# h_drift += B_G / 2 * (sig_1_z + sig_2_z + sig_3_z + sig_4_z)
# this contribution is 0 on the subspace.
h_drift = DenseOperator(h_drift.data[sub_space_ind])
h_ctrl = [DenseOperator(np.zeros((2**4, 2**4))) for _ in range(3)]
import numpy as np
from qopt.matrix import DenseOperator
from qopt.energy_spectrum import plot_energy_spectrum
pauli_z = DenseOperator(np.asarray([[1, 0], [0, -1]]))
pauli_x = DenseOperator(np.asarray([[0, 1], [1, 0]]))
tau_z = pauli_z.kron(pauli_z.identity_like())
tau_x = pauli_x.kron(pauli_x.identity_like())
sigma_z = (pauli_z.identity_like()).kron(pauli_z)
sigma_x = (pauli_x.identity_like()).kron(pauli_x)
sigma_x_tau_x = pauli_x.kron(pauli_x)
def example_hamiltonian_flopping(detuning):
hamiltonian = []
t_c = 20
e_z = 24
g_mu_b_b_x = 15
g_mu_b_b_z = 4
for eps in detuning:
omega = np.sqrt(eps**2 + (2 * t_c)**2)
theta = np.arctan(eps / (2 * t_c))
hamiltonian.append(.5 * omega * tau_z + (e_z / 2) * sigma_z -
(g_mu_b_b_x / 2) * sigma_x *
(np.cos(theta) * tau_x - np.sin(theta) * tau_z) -
(g_mu_b_b_z / 2) * sigma_z *
(np.cos(theta) * tau_x - np.sin(theta) * tau_z))
return hamiltonian