colission model for regular and random injection

[Muhammad Saleh]

I have a system that all-qubit systems, both the target and

Ancilla are qubits in collision model. The arrival times of the ancilla qubits to the collision region and see the effects on the

preparation time of the target state. I wanna compare two extreme

cases like ancilla arrives periodically, at regular

time intervals, versus they arrive completely

randomly. I know random times can be selected from

Poisson distribution. Collision model numerical simulation should

offer a simple and flexible approach. I would expect it leads to non-markovian dynamics, but I don't know how exactly apply these in the code. i would appreciate your help in advance 

times = np.linspace(0, 0.05, 20)  
kmax = 3000  #k_colision
ancilla_temp = 1.0  


sz = tensor(sigmaz(), qeye(2))
sm = tensor(sigmam(), qeye(2))
sp = tensor(sigmap(), qeye(2))
sz0 = tensor(qeye(2), sigmaz())  
sm0 = tensor(qeye(2), sigmam())
sp0 = tensor(qeye(2), sigmap())

H_int = (sm0 * sp + sp0 * sm) +  (sz0 * sz)


rho_ancilla_thermal = thermal_dm(2, 1 / ancilla_temp)

alpha = 1 / (2**0.5)
beta = 1 / (2**0.5)


psi = alpha * basis(2, 0) + beta * basis(2, 1)

rho_target= psi.proj()
rho0 = tensor(rho_ancilla_thermal, rho_target)

coherence_list = []
klst = []

for _ in range(kmax):

    rho = mesolve(H_int, rho0, times)

    rhof = (rho.states)[-1].ptrace(1)
   
    coherence = abs(rhof[0, 1]) + abs(rhof[1, 0])  
    coherence_list.append(coherence)


    rho0 = tensor(rho_ancilla_thermal, rhof)
    klst.append(_ + 1)