stochastic wave-function evolution of the quantum Langevin equation

[hamids...@gmail.com]

Hii all,

I need to simulate Eq.  4 in the picture below, and i  don't know which functions (mesolve, mcsolve, smesolve, ssesolve) i  have to use for my simulation. Please, I need someone to help me. 

Thank  you  

[ANIRUDDHA CHAKRABORTY]

I guess it should be mesolve for solving Lindblad equation but Linblad is Markovian (i.e time correlation is much smaller than system evolution time) 

Aniruddha

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[Hamid Sakhouf]

First of all, I would like to thank you for your  reply.   But how  can I implement   the white noise using  mesolve 

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[Éric Giguère]

There is no solver for that exact equation, you will need to force it...

sesolve could be used with:

noise_array =  np.random.randn(N_dts) # **0.5?

H = H0 - 0.5j * L.dag() @ L +1j * L * Coefficient(lambda t, noise: noise, args={"noise": noise_array[0])

solver = SESolver(H, options={ "method": "vern7", "interpolate": False}) # Default "adams" method remember data between steps.

solver.start(psi_0, t_0)

for i, t in enumerate(np.linspace(t_0, t_final, dt)):

    state = solver.step(t + dt, args={"noise": noise_array[i]}) # evolve from t to t+dt and return the state at t+dt.

This will do the evolution with in chunks of `dt` with a different noise value for each steps.

`"interpolate": False` with verner method ensure each steps start from a clean state with the new noise value.

With just the limited info you shared, this seems a somewhat easy and promising method.

[Hamid Sakhouf]

Thank you so much. This equation form this paper: https://arxiv.org/abs/2501.10349v1

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[Hamid Sakhouf]

Hi there,

I've been using the ssesolve function (qt.ssesolve(

                H,

                psi0,              

                t_list,

                sc_ops=[L_stochastic],  # Single collapse operator

                e_ops=e_ops,

                heterodyne=True,

                ntraj=500,  # Increased for better statistics

                options={

                    "dt": 0.0125,  # Larger time step for stability

                    "store_measurement": True,

                   

                   "store_states": False,

                    "map": "serial",  # Use serial for stability

                    "normalize_output": True,

                    "method": "platen"  # Explicit method specification

                }

            ))  for my quantum simulation work, and I've obtained results that are generally in line with what I need. However, I've encountered an unexpected behavior: when comparing results for γ=0 (no dissipation) versus γ≠0 (with dissipation), the SRE (Symmetric Relative Entropy) values for γ=0 are lower than those with γ≠0.

Based on my understanding, I would expect the opposite trend. Please help me understand why this might be happening or suggest ways to investigate this further.

Thank you for your assistance

[Éric Giguère]

If you look at the equation of ssesolve: https://qutip.readthedocs.io/en/stable/guide/dynamics/dynamics-stochastic.html#equation-jump-ssesolve

It's close to yours, but there are extra terms. It would be the same if the `e_n` were zeros.

(dW is the white noise).

You should check that the right physic is simulated for your problem. 

[Hamid Sakhouf]

Thank you so much, Eric, for this clarification. 

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