arbitrary evolution for part of the system

[Krastanov]

In many cases when working with error corrected system, I want to optimize for a mapping:

|A⟩⊗|B1⟩ ↦ |C⟩⊗|D1⟩
|A⟩⊗|B2⟩ ↦ |C⟩⊗|D2⟩
|A⟩⊗|B3⟩ ↦ |C⟩⊗|D3⟩

Where the B and D vectors are fixed, but I do not care about what the A and C vectors are (and they can even be optimization variables).

Is that feasible?

[andgoldschmidt]

Yes, definitely possible. We can write a custom loss function over NonlinearKnotPointObjective that computes just the fidelity of the subspace spanned by $B_j \rightarrow D_j$. Then, we use this as the cost instead of the full fidelity.

• Is it necessary that $B_j \rightarrow D_j$ is accomplished jointly $\forall j$?
• Does $A \rightarrow C$ have to be the same mapping $\forall j$, even if we don't care what it is?

[Krastanov]

Is there some user-facing documentation on how to write custom loss functions?

[andgoldschmidt]

Quantum objectives can help navigate writing custom losses via examples. The main idea is to call KnotPointObjective from DirectTrajOpt.jl

The problem templates in QuantumCollocation.jl are also a good place to see. Most of our documentation is about using problem templates. More should be added.