Optimal quantum control with poor statistics

TL;DR

This paper introduces a Bayesian optimization-based control algorithm for quantum systems that effectively handles high measurement noise and single-shot data, reducing experimental effort in quantum control tasks.

Contribution

It presents a novel quantum control method that operates efficiently with poor statistical data, surpassing traditional approaches reliant on accurate measurements.

Findings

Successfully controls quantum systems with high shot noise

Achieves optimal control with minimal experimental repetitions

Demonstrates effectiveness in both numerical and experimental setups

Abstract

Control of quantum systems is a central element of high-precision experiments and the development of quantum technological applications. Control pulses that are typically temporally or spatially modulated are often designed based on theoretical simulations. As we gain control over larger and more complex quantum systems, however, we reach the limitations of our capabilities of theoretical modeling and simulations, and learning how to control a quantum system based exclusively on experimental data can help us to exceed those limitations. Due to the intrinsic probabilistic nature of quantum mechanics, it is fundamentally necessary to repeat measurements on individual quantum systems many times in order to estimate the expectation value of an observable with good accuracy. Control algorithms requiring accurate data can thus imply an experimental effort that negates the benefits of avoiding theoretical modeling. We present a control algorithm based on Bayesian optimization that finds optimal control solutions in the presence of large measurement shot noise and even in the limit of single-shot measurements. With several numerical and experimental examples we demonstrate that this method is capable of finding excellent control solutions with minimal experimental effort