[Feature]: Embedded operators for control problems and fidelity

[andgoldschmidt]

What happened?

There is no subspace information in a control problem.

Consider a three level transmon

η = -0.2
a = annihilate(3)
sys = QuantumSystem(η / 2 * a'*a'*a*a, [(a + a') / 2, -im*(a - a') / 2])

and solve a control problem with an embedded operator

T = 50
Δt = 0.2
U_goal = EmbeddedOperator(GATES[:X], sys)
prob = UnitarySmoothPulseProblem(sys, U_goal, T,  Δt)

The fidelity is not computed in the subspace by default:

|julia> unitary_fidelity(prob)
0.6666...

|julia> unitary_fidelity(prob, subspace=get_subspace_indices(1:2, 3))
0.9999...

Version

stable release

What does this bug affect?

• quantum system construction
• problem setup
• problem solution
• problem performance
• solution analysis
• plotting
• documentation
• tests
• other (please specify below)

Other information

No response

[andgoldschmidt]

My preferred solution would be to add U_goal to the fields of

mutable struct QuantumControlProblem <: AbstractProblem
...

in problems.jl, then make the adaptations to unitary_fidelity, and add appropriate tests to preserve this behavior.

[andgoldschmidt]

Two utilities that would benefit from this change:

1. unitary_fidelity
2. is_reachable