Driving High-Fidelity Many-Body Matrix Product State Dynamics with Exact Gradient Quantum Optimal Control

The comprehensive demand for precise, high-fidelity control in high-dimensional Hilbert spaces places increasing emphasis on the role of optimization methodologies and their performance capacities. Here, we apply recently established optimal control techniques -- utilizing the somewhat counter-intuitive fact that appropriate dynamical approximations lead to more precise and significantly cheaper implementation of optimal control than a full dynamical solution -- to a many-body problem within the matrix product state ansatz at system sizes completely beyond the reach of exact diagonalization approaches. We obtain fidelities in the range 0.99-0.9999 and beyond with unprecedented efficiency and find associated quantum speed limit estimates. Benchmarking against earlier, seminal derivative-free work on similar problems, we show that the simpler optimization objectives employed therein are not sufficient for fulfilling high-fidelity requirements, and find substantial qualitative differences in the optimized dynamics (bang-bang structures) and associated quantitative performance improvements (orders of magnitude) and transformation times (factor three) depending on the comparative measure. This demonstration paves the way for efficient high-fidelity control of very high-dimensional systems which has hitherto not been possible.