Optimal Quantum Control

We present ELQ (Efficiently Learning Quantum systems), an open-source framework for designing optimal quantum control schemes that achieve high-fidelity gate operations. Our method leverages automatic differentiation and GPU acceleration in JAX to efficiently compute gradients through realistic experimental constraints, including bandwidth limitations, non-linear transmission functions, and environmental noise. We demonstrate ELQ's capabilities by optimizing single-, simultaneous single-, and two-qubit gates for hole spins in silicon quantum dots. By incorporating numerically sampled noise trajectories, we develop control pulses that are robust to both high-frequency noise from ensembles of two-state fluctuators (1/f noise) and quasi-static errors from charge and magnetic field variations. Our results show that pulses optimized for simultaneous single-qubit operations significantly outperform those designed for sequential operation, highlighting the importance of considering cross-talk and unwanted coupling effects. The ELQ codebase enables the broader quantum computing community to design and optimize high-fidelity quantum gates while accounting for device-specific constraints and noise environments.