Hessian-based optimization of constrained quantum control

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 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 second-order analytical derivatives of the coherent dynamics and find improvements compared to the standard of optimizing with the approximate second-order Broyden-Fletcher-Goldfarb-Shanno algorithm. We demonstrate performance improvements for both the best and the average errors of constrained unitary gate synthesis on a circuit-QED system over a broad range of different gate durations.