def get_Lindbladian(self, dims):
"""
Compute the Lindbladian, based on relaxation, dephasing constants and finite temperature.
Returns
-------
tf.Tensor
Hamiltonian
"""
Ls = []
if "t1" in self.params:
t1 = self.params["t1"].get_value()
gamma = (0.5 / t1) ** 0.5
L = gamma * self.collapse_ops["t1"]
Ls.append(L)
if "temp" in self.params:
if self.params["temp"].get_value().numpy():
if self.hilbert_dim > 2:
freq_diff = np.array(
[
(
self.params["freq"].get_value()
+ n * self.params["anhar"].get_value()
)
for n in range(self.hilbert_dim)
]
)
else:
freq_diff = np.array([self.params["freq"].get_value(), 0])
beta = 1 / (self.params["temp"].get_value() * kb)
det_bal = tf.exp(-hbar * tf.cast(freq_diff, tf.float64) * beta)
det_bal_mat = hskron(
tf.linalg.tensor_diag(det_bal), self.index, dims
)
L = gamma * tf.matmul(self.collapse_ops["temp"], det_bal_mat)
Ls.append(L)
if "t2star" in self.params:
gamma = (0.5 / self.params["t2star"].get_value()) ** 0.5
L = gamma * self.collapse_ops["t2star"]
Ls.append(L)
if Ls == []:
raise Exception("No T1 or T2 provided")
return tf.cast(sum(Ls), tf.complex128)
def get_Lindbladian(self, dims):
"""
Compute the Lindbladian, based on relaxation, dephasing constants and finite
temperature.
Returns
-------
tf.Tensor
Hamiltonian
"""
# Form of the operators from p. 71 in https://ocw.mit.edu/courses/
# nuclear-engineering/22-51-quantum-theory-of-radiation-interactions-fall-2012/
# lecture-notes/MIT22_51F12_Ch8.pdf
Ls = []
if "t1" in self.params:
t1 = self.params["t1"].get_value()
gamma = (0.5 / t1)**0.5
L = gamma * self.collapse_ops["t1"]
Ls.append(L)
if "temp" in self.params:
if self.hilbert_dim > 2:
freq = self.params["freq"].get_value()
anhar = self.params["anhar"].get_value()
freq_diff = np.array(
[freq + n * anhar for n in range(self.hilbert_dim)])
else:
freq_diff = np.array([self.params["freq"].get_value(), 0])
beta = 1 / (self.params["temp"].get_value() * kb)
det_bal = tf.exp(-hbar * tf.cast(freq_diff, tf.float64) * beta)
det_bal_mat = hskron(tf.linalg.tensor_diag(det_bal),
self.index, dims)
L = gamma * tf.matmul(self.collapse_ops["temp"], det_bal_mat)
Ls.append(L)
if "t2star" in self.params:
gamma = (0.5 / self.params["t2star"].get_value())**0.5
L = gamma * self.collapse_ops["t2star"]
Ls.append(L)
if Ls == []:
raise Exception("No T1 or T2 provided")
return tf.cast(sum(Ls), tf.complex128)