RFC: time-dependent operator macro

[aryavorskiy]

Currently the only time-dependent operator type present in the library is TimeDependentSum, which is actually a lazy sum with time-dependent coefficients. While certainly useful, it might be a bit hard and unintuitive to use in code. My proposal is the following:

• Write a macro that will create time-dependent operators in a convenient manner like A = @timedependent t -> (B * t + C * (1 - t)) ⊗ D(t - 2). It does approximately the following:
  • All +, *, ⊗ top-level calls are turned into lazy operators.
  • dense, sparse e. g. calls are left untouched
  • All other calls are checked for time-dependent operators like D(t - 2). If the call is a time-dependent operator, we create a CompositeTimeDependentOperator with t -> t - 2 as a time parameter. If it is an ordinary function, we treat it as a number (because in context of this macro we expect an operator or a number, nothing else)

Also maybe this architecture should support parameters other than time (e. g. magnetic field?).
Hope you find this idea useful.

[Krastanov]

This can be quite valuable. My main worry if we go in this direction would be diverging too much from SciMLOperators https://docs.sciml.ai/SciMLOperators/stable/

[amilsted]

This is an interesting idea! I think it could be compatible with a SciMLOperators approach to time-dependent operators. Seems like a layer on top of all that? By the way, even as things are, it should be possible to make lazy sums and products of time-dependent operators and have them behave properly. They won't be AbstractTimeDependentOperators themselves, but they should respond to set_time! properly and work when used in schroedinger_dynamic and co.

You can't currently have LazyTensors of time-dependent stuff, however.