Optimal control in disordered quantum systems

We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast high-fidelity transport can be achieved using protocols designed with differentiable programming. Building on this, we then show how this approach can be effectively adapted to control a disordered quantum system. We consider two settings: optimal control for a known unwanted disorder pattern, i.e., a specific disorder realisation, and optimal control where only the statistical properties of disorder are known, i.e., optimizing for high average fidelities. In the former, disorder effects can be effectively mitigated for an appropriately chosen control protocol. However, in the latter setting the average fidelity can only be marginally improved, suggesting the presence of a fundamental lower bound.