Analytic Filter-Function Derivatives for Quantum Optimal Control

Autocorrelated noise appears in many solid-state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of is often less efficient than approximate methods. Here, we focus on the filter function formalism, which allows computation fidelities presence autocorrelated classical noise. Hence, formalism can combined with optimal control algorithms design pulses, optimally implement gates. To enable use gradient-based fast convergence, present analytically derived gradients respect pulse amplitudes, analyze computational complexity our results. When comparing optimization using derivatives a gradient-free approach, find that method roughly 2 orders magnitude faster test cases. We also provide modular implementation compatible packages.