Characterization of a driven two-level quantum system by Supervised Learning

TL;DR

This paper explores using supervised learning, specifically neural networks, to characterize a driven two-level quantum system, accurately mapping control parameters to system states without prior knowledge.

Contribution

It demonstrates the effectiveness of neural networks in modeling quantum system dynamics and highlights the limitations in indirect estimation scenarios.

Findings

High-precision mapping when offset is known

Challenges in indirect estimation of the distance to target

Limits of neural network interpolation based on mapping properties

Abstract

We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.