Support custom fidelities

[flowerthrower]

Introduce a FidelityComputer class (see qutip-qtrl) for custom fidelity types.

[MatthewBelzer]

Hello,

I am working on a problem where I am interested in doing Quantum Optimal Control on a subsystem of a Hamiltonian that is comprised of two coupled systems. To do this numerically in QuTiP, as I understand it, I would have to use a custom Fidelity Computer with CRAB/GRAPE and use it to take a partial trace of the wave vector to get the wave vector of the subsystem that I am interested in. And then, I would have to optimize that using CRAB/GRAPE.

After searching the QuTiP forum, I have found one thread on custom Fidelity Computers, but it is not recent and the code it links to has errors when I run it. I have tried to update the code (see Jupyter File attached to my QuTiP forum post), and I am now getting an error that says:

UsageError: 'No fid_computer (Fidelity computer) set. A default should be assigned by the Dynamics subclass'

Any help on solving this issue and/or implementing a custom fidelity would be appreciated.

Thanks,
Matthew

[hodgestar]

@flowerthrower @ajgpitch Do either of you know off hand how you think this should be implemented?