Quantum reservoir complexity by Krylov evolution approach

TL;DR

This paper introduces a Krylov evolution-based method to quantitatively assess and optimize the complexity of quantum reservoirs, enhancing their performance in quantum machine learning tasks on NISQ devices.

Contribution

It presents a novel, physically grounded Krylov complexity approach to evaluate and improve quantum reservoir design for machine learning applications.

Findings

Krylov complexity correlates strongly with quantum reservoir performance.

The method provides a quantitative tool for designing better quantum reservoirs.

Enhances the implementation of effective quantum machine learning algorithms.

Abstract

Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the NISQ era, because of its superb performance and compatibility with current quantum devices. By harnessing the properties and dynamics of a quantum system, quantum reservoir computing effectively uncovers hidden patterns in data. However, the design of the quantum reservoir is crucial to this end, in order to ensure an optimal performance of the algorithm. In this work, we introduce a precise quantitative method, with strong physical foundations based on the Krylov evolution, to assess the wanted good performance in machine learning tasks. Our results show that the Krylov approach to complexity strongly correlates with quantum reservoir performance, making it a powerful tool in the quest for optimally designed quantum reservoirs, which will pave the road to the implementation of successful quantum machine learning methods.