Combining machine-learning characterization and quantum optimal control to improve superconducting qubit operations*

Quantum optimal control theory offers a powerful toolbox to design pulse shapes that can realize, in numerical simulations, desired quantum operations with extremely high fidelity. When implementing these pulses in practice, however, the benefit of using optimal pulses over simple analytical forms is often greatly reduced. A significant part of this discrepancy can be attributed to failures of the numerical model to precisely capture the complete quantum dynamics generated by the control electronics. Here, we address this issue directly by building a framework where we break down the problem of realizing high-fidelity quantum operations into two parts. First, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimental data. We investigate a range of trainable models from black-box neural networks to physically informative Lindblad master equation solvers. Second, we use such a trained numerical model in combination with state-of-the-art quantum optimal control to find pulse shapes that realize quantum gates with maximal accuracy given our experimental constraints. Using numerical simulations, we show the feasibility of learning from realistically available data to accurately characterize qubit dynamics and to discover high-fidelity arbitrary single-qubit gates. We then demonstrate our framework in an experimental setting by optimizing the Clifford gate set of a superconducting transmon qubit.