Hessian-based optimization of constrained quantum control

TL;DR

This paper develops and implements exact second-order derivatives for quantum control optimization, improving the efficiency and accuracy of gate synthesis in quantum systems compared to approximate methods.

Contribution

It introduces exact second-order derivative calculations for quantum control, enhancing optimization performance over traditional approximate methods.

Findings

Improved optimization accuracy for quantum gate synthesis.

Enhanced performance over approximate second-order methods.

Demonstrated benefits across various gate durations.

Abstract

Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds. A standard tool for optimizing simulated quantum dynamics is the gradient-based \textsc{grape} algorithm, which has been successfully applied in a wide range of different branches of quantum physics. In this work, we derive and implement exact $2^{\mathrm{nd}}$ order analytical derivatives of the coherent dynamics and find improvements compared to the standard of optimizing with the approximate $2^{\mathrm{nd}}$ order \textsc{bfgs}. We demonstrate performance improvements for both the best and average errors of constrained unitary gate synthesis on a circuit-\textsc{qed} system over a broad range of different gate durations.