Engineering quantum reservoirs through Krylov complexity, expressivity, and observability

This study employs Krylov-based information measures to understand task performance in quantum reservoir computing, a subfield of quantum machine learning. In our study, we show that fidelity and spread complexity can only explain the task performance for short time evolutions of the quantum systems. We then discuss two measures, Krylov expressivity and Krylov observability, and compare them to task performance and the information processing capacity. Our results show that Krylov observability exhibits almost identical behavior to information processing capacity, while being three orders of magnitudes faster to compute. In the case when the system is undersampled, Krylov observability best captures the behavior of the task performance.