Optimized Bayesian System Identification in Quantum Devices

Identifying and calibrating quantitative dynamical models for physical quantum systems is critical in the development of a quantum computer. We present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a dynamical model, using optimised experimental “probe” controls and measurement. The estimation algorithm is based on a Bayesian particle filter, and is designed to autonomously choose informationally-optimised probe experiments with which to compare to model predictions. In both simulated and experimental demonstrations, we see that successively longer pulses are selected as the posterior uncertainty iteratively decreases, leading to an exponential scaling in the accuracy of model parameters with the number of experimental queries. In an experimental calibration of a single qubit ion trap, we achieve parameter estimates in agreement with standard calibration approaches but requiring ∼ 20× fewer experimental measurements. We also demonstrate the performance of the algorithm on multi qubit superconducting devices, demonstrating the flexibility of these techniques.