Assistance needed

[Hmd 2015]

Dear all,

I am trying to implement the stochastic master equation shown below.

I think the stochastic term can be implemented using sc_ops in smesolve (flame  it  in Eq. with  Red  line). However, I am unsure how to implement the highlighted (yellow) term, which represents the action of the jump operators on the density matrix through a double anticommutator, together with antidephasing.

I would appreciate any guidance on how to include this term correctly in the simulation.

Thank you very much for your help.

Best regards,
Hmd

[Éric Giguère]

This is very close to the default smesolve equation: https://qutip.readthedocs.io/en/stable/guide/dynamics/dynamics-stochastic.html#stochastic-master-equation

If L is hermitian, you probably can use it as is (there is an extra `-tr(L @ rho + rho @ L)`), (not sure if H is expected to be hermitian, test properly).

If this does not work, then it would be hard to use qutip's solvers, we don't have generic stochastic solver taking arbitrary function / operators.

Qutip has SODE that could be used, but the interface is not user facing: it's not documented and has some hard coded parts for the existing solvers...

If you need it and are not in an hurry, you could ask it as a new feature on github.

If you want to try to do it yourself, something like:

```

L = # drift as a super operator QobjEvo (even if constant)

c = [ ] # list of diffusion operators super operator QobjEvo

integrator = PlatenSODE(SimpleStochasticSystem(-1j * L, c), options={"dt": 0.001, "tol": 1e-10})

integrator.start(tlist[0], qutip.operator_to_vector(rho0).data)

for t in tlist[1:]:

    t_step, data_t = integrator.run(t)

    out.append(qutip.Qobj(data_t), dims=rho0.dims)

```

I did not try this code snippet, it probably need some debugging.

Hope it help

Eric