Simulation-Driven Bayesian Hamiltonian Learning for Autonomous Characterization and Control of Spin-Defects

High-fidelity, coherent control of quantum systems requires detailed knowledge about the system's underlying Hamiltonian and significant device-specific calibration. This is usually approached via simple pulse protocols (e.g., combinations of control impulses and idling) which describe various experiments such as Ramsey and Rabi measurements. These simple protocols, however, represent an exceedingly small set of possible control choices from which to learn system parameters. In this work we explore the full space of quantum controls and assess their utility in autonomous control and Hamiltonian learning tasks through explicit simulation of the underlying quantum dynamics incorporated into the learning process. We focus our study on autonomous characterization and control of electron spin-defects like the nitrogen-vacancy center in diamond, leveraging open-source control hardware and Bayesian inference software to assess these simulation-driven experiments. We quantify the information theoretic value of different protocols and demonstrate how these techniques can be used for the large-scale, autonomous control of electron spin-defects.