Characterization of a Driven Two-Level Quantum System by Supervised Learning
Résumé
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.