def lindbladian_population(U_dict: dict, lvl: int, gate: str):
U = U_dict[gate]
lvls = int(np.sqrt(U.shape[0]))
psi_0 = tf.constant(basis(lvls, 0), dtype=tf.complex128)
dv_0 = tf_dm_to_vec(tf_state_to_dm(psi_0))
dv_actual = tf.matmul(U, dv_0)
return populations(dv_actual, lindbladian=True)[lvl]
def initialise(self, drift_H, lindbladian=False, init_temp=None):
"""
Prepare the initial state of the system. At the moment finite temperature requires open system dynamics.
Parameters
----------
drift_H : tf.Tensor
Drift Hamiltonian.
lindbladian : boolean
Whether to include open system dynamics. Required for Temperature > 0.
init_temp : Quantity
Temperature of the device.
Returns
-------
tf.Tensor
State or density vector
"""
if init_temp is None:
init_temp = tf.cast(self.params["init_temp"].get_value(),
dtype=tf.complex128)
diag = tf.linalg.diag_part(drift_H)
dim = len(diag)
if abs(init_temp) > np.finfo(
float).eps: # this checks that it's not zero
# TODO Deal with dressed basis for thermal state
freq_diff = diag - diag[0]
beta = 1 / (init_temp * constants.kb)
det_bal = tf.exp(-constants.hbar * freq_diff * beta)
norm_bal = det_bal / tf.reduce_sum(det_bal)
dm = tf.linalg.diag(norm_bal)
if lindbladian:
return tf_utils.tf_dm_to_vec(dm)
else:
raise Warning(
"C3:WARNING: We still need to do Von Neumann right.")
else:
state = tf.constant(qt_utils.basis(dim, 0),
shape=[dim, 1],
dtype=tf.complex128)
if lindbladian:
return tf_utils.tf_dm_to_vec(tf_utils.tf_state_to_dm(state))
else:
return state