def apply_dephasing(number_of_spins, alpha, B):
'''
takes number of spins, alpha, and the magnetic field and returns the
FM hamiltonian along with its ground state and the dephased ground state
'''
calc = ising_calculator_FM(number_of_spins, alpha, B)
H = calc.get_H()
energy,groundstate = H.groundstate()
dm_groundstate = ket2dm(groundstate)
dephased = do_dephasing_dm(dm_groundstate, number_of_spins)
return H, dm_groundstate, dephased
def calculate_and_save():
quant = state_quantifier(number_of_spins)
ground_states = []
for i,B in enumerate(B_list):
print i
calc = ising_calculator_FM(number_of_spins, alpha, B)
H = calc.get_H()
energy,groundstate = H.groundstate()
ground_states.append(groundstate)
sx,sy,sz = quant.get_reduced_dms(ground_states, spin = 0)
np.save('magnetization_array_one_spin_{}'.format(number_of_spins), (B_list,sx,sy,sz))
def calculate_and_save():
magnetization_array = np.empty_like(B_list)
quant = state_quantifier(number_of_spins)
for i,B in enumerate(B_list):
print i
calc = ising_calculator_FM(number_of_spins, alpha, B)
H = calc.get_H()
energy,groundstate = H.groundstate()
m = quant.absolute_magnetization_x(groundstate)
magnetization_array[i] = m
np.save('magnetization_array_{}'.format(number_of_spins), magnetization_array)
def calculate_and_save():
quant = state_quantifier(number_of_spins)
ground_states = []
for i, B in enumerate(B_list):
print i
calc = ising_calculator_FM(number_of_spins, alpha, B)
H = calc.get_H()
energy, groundstate = H.groundstate()
ground_states.append(groundstate)
sx, sy, sz = quant.get_reduced_dms(ground_states, spin=0)
np.save('magnetization_array_one_spin_{}'.format(number_of_spins),
(B_list, sx, sy, sz))
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
#constructing a list of operators sx_list and sy_list where
#the operator sx_list[i] applies sigma_x on the ith particle and
#identity to the rest
sx_list = []
sy_list = []
for n in range(N):
op_list = []
for m in range(N):
op_list.append(si)
op_list[n] = sx
sx_list.append(tensor(op_list))
op_list[n] = sy
sy_list.append(tensor(op_list))
calc = ising_calculator_FM(number_of_spins, alpha, B)
H = calc.get_H()
# energy,state = H.groundstate()
# print 'groundstate energy', energy
# print 'groundstate expectation', expect(sx_list[0], state)
# print 'groundstate expectation', expect(sx_list[1], state)
# print 'groundstate expectation', expect(sx_list[2], state)
# print state[0:10]
# print state.dag() * H * state
# print expect(H, state)
# print state[0:10]
# print state.norm()
# print expect(sx_list[3] , state)
energies, states = H.eigenstates()
print energies[0:2]