Coherent state information in `dsf_mesolve`.

[oameye]

After you run dsf_mesolve, you don't have access anymore to the parameters of the dynamical shifted fock problem. This is because TimeEvolutionSol does not contain the parameters of "ode problem". However, it would be useful information what the coherent state value was over time (, or at the end of the simulation).

Since dsf_mesolve is a bit underdocumented I had some questions about the implementation:

• Given you provide e_ops, for what are the expectations values evaluated: only the quantum fluctuations or the coherent state + quantum fluctuations?
• After dsf_mesolve does TimeEvolutionSol.states contain only the quantum fluctuations or the coherent state + quantum fluctuations?
• Suppose I would like to do a adiabatic parameter sweep, where I provide the simulation of the next parameter values with the final state of the previous parameter value. Is it enough to only set ψ0=sol_dsf.states[end]? Or should I also somehow give the correct initial condition for the coherent state α0_l?

[albertomercurio]

We should definitely add a detailed documentation about it. Anyhow, we discuss the DSF algorithm in the release paper

• https://arxiv.org/abs/2504.21440

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• Given you provide e_ops, for what are the expectations values evaluated: only the quantum fluctuations or the coherent state + quantum fluctuations?

It stores the coherent + quantum fluctuations. In other words, it measures the same quantity you would measure using the standard mesolve method, with a larger Hilbert space of course.

• After dsf_mesolve does TimeEvolutionSol.states contain only the quantum fluctuations or the coherent state + quantum fluctuations?

Only the quantum fluctuations around the coherent state. That's the power of the DSF algorithm, where the cutoff can be very small in the fluctuations frame.

• Is it enough to only set ψ0=sol_dsf.states[end]? Or should I also somehow give the correct initial condition for the coherent state α0_l?

I would recommend to store the values of alpha using e_ops. Then, you can set α0_l = sol_dsf.expect[end] equal to the last value of the coherence.

It worth mentioning that time dependent Hamiltonian are not yet supported by DSF. I have some idea about it, which should be done using SciMLOperators.j

[oameye]

Thanks a lot for answering the questions. I would be very interested in having time dependent Hamiltonian support for DSF as it would enable me to make linear reponse (S21) plots for comparison with experiment. Could you maybe detail a bit more your idea? I would be willing to start a PR implementing the idea.

[oameye]

I noticed that the QT.jl arxiv paper does not cite where the algorithm was developed. I would like to also like t cite the original work. Could you point me to the right literature?

EDIT:
After a second try I found two sources :):

• https://arxiv.org/pdf/2306.13708
• https://doi.org/10.1103/PRXQuantum.3.010329