Achieving fast high-fidelity optimal control of many-body quantum dynamics

TL;DR

This paper demonstrates an efficient optimal control method for many-body quantum dynamics, achieving high fidelities in a challenging phase transition, with insights into the control protocols and potential for experimental application.

Contribution

It applies an exact-gradient optimal control technique to a complex many-body quantum problem, revealing new control strategies and improving methodological approaches.

Findings

Achieved fidelities between 0.99 and 0.9999

Identified a linear sweep followed by bang-bang control as optimal

Demonstrated exponential fidelity-duration trade-off

Abstract

We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99-0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high-fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control -- in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter.