[Feature]: Convert objectives to constraints

[andgoldschmidt]

Feature Description

Background

There should be utilities that turn any objective into some appropriate constraint. The constraint should take in an objective and a value as arguments, and the output should be a constraint satisfying the desired condition.

For example,

function ObjectiveEqualityConstraint(objective::Objective, value::Float64) 
     objective - value = 0
end

function ObjectiveInequalityConstraint(objective::Objective, value::Float64) 
     objective - value > 0
end

This functionality has already been implemented in FinalUnitaryFidelityConstraint, which follows the format of UnitaryInfidelityObjective; the point of this issue is to generalize and abstract this concept.

Suggested checklist

• Pick a specific objective (e.g. UnitaryInfidelityObjective objective). Write a routine that creates a constraint from this objective. Compare to the existing constraint (e.g. FinalUnitaryFidelityConstraint).

Importance

1 (lowest)

What does this feature affect?

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

Other information

No response

[andgoldschmidt]

This would allow for a much simpler implementation of the constraint class of problem templates like minimum time and robustness. Those problems could extract the existing fidelity objective from the problem params, which by default already "pops" from this list. Then, the constraint could be constructed from this objective using the existing gradients.

The code that computes fidelity and sets up the fidelity constraint in these methods could be mostly replaced.