Plotting ground state populations of instantaneous Hamiltonian

[qflux98]

Instead of plotting state populations w.r.t some fixed operator as described in several Krotov example notebooks (e.g. https://qucontrol.github.io/krotov/v1.0.0/notebooks/01_example_simple_state_to_state.html), how can I plot ground state populations for instantaneous hamiltonian for every time grids after pulse controls are optimized? Do you have relevant example notebooks?

[goerz]

You'd have to sum the nested list that encodes the time-dependent Hamiltonian into a single Qobj, and then call QuTiP's eigenstates method to find the ground state, at every time step.

We don't have an example that does this.

[qflux98]

as an additional question, is there a way to always start from an initial state to be a ground state of H(0) while continuing the optimization procedure from the previous optimization by using continue_from=opt_result? I tried to change the initial state after one optimization is done and used continue_from=opt_result to continue, but then an error occurred because it changed the objective.

[goerz]

If instead of opt_result.objectives[0].mesolve, you meant to write opt_result.optimized_objectives[0].mesolve, then yes, that would run qutip.mesolve using the initial state and the Hamiltonian from the objective (with the optimized fields in the second case).

I'm not sure what you mean in the second question. Isn't H(0) the same in both optimizations?

In general, if the objectives change, you can't use continue_from. That option is for when you want to continue a previous optimization with modified convergence criteria / iter_max.

[qflux98]

are we supposed to fix the boundary conditions of pulse sequence throughout the optimization (in the conventional field of QOC)? If not, I was thinking of a case where your pulse value at t=0 may vary after the first optimization by using some S(t) that is non-zero at t=0 (e.g. S(t) = 1).

[goerz]

Changing the initial state in each iteration like that is not supported. You might be able to get it to work somehow, either via hooks or by doing only a single iteration for each call of optimize_pulses. It seems like a very questionable approach to me, but maybe I’m wrong. In any case, your life will be much simpler if you keep S(t) = 0 at the boundaries in this scenario

[qflux98]

You're absolutely right. In fact, my question is coming from wondering whether for a very large annealing time T, if you don't change your final value of pulse schedule, which means always fixing the final Hamiltonian, then this might cause a training problem due to the adiabaticity of the system (The final state should be in the ground state of the final Hamiltonian that is fixed)