Add writeup about Hamiltonian bases and frame transformations

[shaimach]

Is your feature request related to a problem? Please describe.

There is a non-trivial issue relating to the basis and frame which are used to simulate dynamics:

• The Hamiltonian can be in either the dressed or product basis:

  • Thermalization is (probably) always defined in the dressed basis (not sure what happens if different qubits are coupled to different baths with different temperatures).
  • Readout is currently assumed to be in the dressed basis (until Thorge will implement something more refined).

• The Hamiltonian can be represented inone of (at least) 3 frames:

  • The lab frame
  • The frame rotating with the control drive LO (local oscillator)
  • The frame rotating with the qubit

• "The frame rotating with the qubit" can refer to either the qubit as defined in the product basis or the dressed basis

This whole subject is quite confusing.

Describe the solution you'd like
We need a good write-up to explain this to ourselves.

Describe alternatives you've considered
We find a pre-existing write-up which exactly addresses this issue

Additional context
After we have everything laid out in a clear fashion, we can decide how we want this understanding to be reflected in the code. For example:

• The code may support doing the dynamics in one of several frames, as preferred by the user; or
• We can choose one frame and allow the user to transform a state to any of the other frames for plotting; or ...

But that will be a separate discussion