def apply_dephasing(number_of_spins, alpha, B,fm_str = 'AFM',kT = 0.0):
'''
takes number of spins, alpha, and the magnetic field and returns the
hamiltonian along with its ground state and the dephased ground state
choose fm_str = 'FM' for ferromagnetic interaction, and 'AFM' for anti-ferromagnetic
'''
if fm_str == 'FM':
calc = ising_calculator_FM(number_of_spins, alpha, B)
elif fm_str == 'AFM':
calc = ising_calculator_AFM(number_of_spins, alpha, B)
H = calc.get_H()
if kT == 0.0:
energy,groundstate = H.groundstate()
dm_groundstate = ket2dm(groundstate)
else:
Hdata = H.data.todense()
arr_mp = mp.matrix(-Hdata /kT)
exp_mp = mp.expm(arr_mp)
trace = np.array(exp_mp.tolist()).trace()
normalized_mp = exp_mp / trace
normalized_np = np.array(normalized_mp.tolist(), dtype = np.complex)
dm_groundstate = Qobj(normalized_np, dims = 2 * [number_of_spins*[2]])
dephased = do_dephasing_dm(dm_groundstate, number_of_spins)
return H, dm_groundstate, dephased
'''test the dephasing''' #example with diagonal reduced density matrix # up_y = Qobj([[1],[1.j]]).unit() # down_y = Qobj([[1],[-1.j]]).unit() # state = tensor(up_y, down_y) + tensor(down_y, up_y) # state = state.unit() # correlated = ket2dm(state) # print correlated # print do_dephasing_dm(correlated, 2) #example with a non-diagonal density matrix si = qeye(2) up_x = Qobj([[1],[1]]) up_z = basis(2,0) down_z = basis(2,1) m = ket2dm((tensor(up_z, up_x) + tensor(up_x, up_z)).unit()) print do_dephasing_dm(m, 2) red = m.ptrace(0) energies,(state0,state1)= red.eigenstates() R1 = tensor(state0, si) * tensor(up_z.dag(), si) R2 = tensor(state1, si) * tensor(down_z.dag(), si) rot = (R1 + R2).dag() * m * (R1 + R2) dephased_rot = do_dephasing_dm(rot, 2) print dephased_rot dephased_back = (R1 + R2) * dephased_rot * (R1 + R2).dag() print dephased_back
from qutip import basis, Qobj, tensor, ket2dm, qeye import numpy as np '''test the dephasing''' #example with diagonal reduced density matrix # up_y = Qobj([[1],[1.j]]).unit() # down_y = Qobj([[1],[-1.j]]).unit() # state = tensor(up_y, down_y) + tensor(down_y, up_y) # state = state.unit() # correlated = ket2dm(state) # print correlated # print do_dephasing_dm(correlated, 2) #example with a non-diagonal density matrix si = qeye(2) up_x = Qobj([[1], [1]]) up_z = basis(2, 0) down_z = basis(2, 1) m = ket2dm((tensor(up_z, up_x) + tensor(up_x, up_z)).unit()) print do_dephasing_dm(m, 2) red = m.ptrace(0) energies, (state0, state1) = red.eigenstates() R1 = tensor(state0, si) * tensor(up_z.dag(), si) R2 = tensor(state1, si) * tensor(down_z.dag(), si) rot = (R1 + R2).dag() * m * (R1 + R2) dephased_rot = do_dephasing_dm(rot, 2) print dephased_rot dephased_back = (R1 + R2) * dephased_rot * (R1 + R2).dag() print dephased_back
