[Feature]: Sample-based robust control

[andgoldschmidt]

Feature Description

Quantum collocation currently has a UnitaryRobustnessProblem, which can be used to make a control solution robust to an error operator. However, there is more than one way to make a control solution robust. For this feature request, we want to implement sampling-based robust control problem template (see also, Reference [1])

Suppose we have a qubit system $H(t) = \zeta Z + a(t) X$, where $\zeta \sim \mathcal{N}(\mu=0.01, \sigma=0.05)$. That is, we know that there is some dephasing noise on the qubit, and we even characterized the distribution! To implement sampling based robust control, we want to find the best control for the qubit, in expectation. This can be accomplished by drawing samples $\zeta_i$, and constructing an ensemble of quantum systems $H_i(t)$. The goal of the problem template is to maximize the expected fidelity of the sampling-based robust control by solving each of the control problems simultaneously.

To accomplish this using Quantum Collocation, follow the QuantumSmoothPulseProblem template, but make the following changes:

1. Instead of passing a static quantum system, the user should pass a function that takes in a list of parameters and outputs a quantum system object from QuantumSystems.
2. The template should have the user pass a distribution and number of samples, or a list of samples, which the template will use to make an ensemble of quantum systems.
3. Make a named trajectory which includes separate unitary components for each system in the ensemble, but a shared control.
4. Attach dynamics constraints for each system in the ensemble.
5. Modify the fidelity cost to be fidelity, in expectation.

Requirements

Tests of the problem template should be implemented.

Importance

1 (lowest)

What does this feature affect?

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

Other information

A relevant example for this type of problem template is control uncertainty, $H(t) = a(t) + \delta a X$, which cannot be captured using the previous robustness framework. It would be cool to make a comparison!

References

[1] Sampling-based Learning Control for Quantum Systems with Uncertainties