  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.

Quantum Physics;Disordered Systems and Neural Networks;Statistical Mechanics