Speed up of time evolution of simple Hamiltonian

[wgo...@googlemail.com]

Hello QuTiP,

This is probably a question, which is probably not so  intersting, 

because it concerns a Hamiltonian, which is very simple.

I'm trying to calculate the free evolution of a qubit

under a AC field which goes like H(t) = alpha(t) * sigma_z

with a initial state lying in the equatorial plane of the Bloch sphere.

The prefactor is defined through alpha(t) = gamma * sin(omega*t).

I calculate the free evolution using mesolve and a string based Hamiltonian.

Thanks for the feature btw. This brought a great speedup. 

exp_lists = mesolve(H_free_c, t, c_ops,

                    args=args)

For 1000 points this takes about 2 seconds and I wonder if I this can be somehow 

speed up. Of course for this simple Hamiltonian I can just integrate the additional 

phase factor myself, but I thought about extending it by using master equations

and introducing decoherence through bath, which was my original intention of

using QuTiP.

Greetings

[nonher...@gmail.com]

Sure, for a system as simple as a qubit then yes things could be made faster. The main thing to do would be to use dense matrices instead of sparse ones for small systems. However, we have 300+ functions that assume a sparse format, so supporting such a change is nontrivial. Moreover, there are several other things behind the scenes that take a but of time. For example, there is a Python call between the ode solver and the RHS function that is likely non trivial for such a small system. That being said, once you start going to larger systems, and adding dissipation then these issues go away. 

-P

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[wgo...@googlemail.com]

Ok no problem, 

just wondered if something like that existed. 

Thanks for the explanation. 

Greetings