Exponential concentration and symmetries in Quantum Reservoir Computing

TL;DR

This paper investigates how Hamiltonian symmetries can mitigate exponential concentration in quantum reservoir computing, enhancing its scalability and robustness for time-series processing.

Contribution

It introduces a method to leverage Hamiltonian symmetries to suppress concentration effects in quantum reservoir computing, improving performance and scalability.

Findings

Symmetries significantly reduce concentration effects.

Robust QRC implementations become feasible with symmetry exploitation.

Concrete examples demonstrate practical benefits.

Abstract

Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as barren plateaus and local minima. The exponential number of independent features of quantum reservoirs opens the way to a potential performance improvement compared to classical settings. However, this exponential scaling can be hindered by exponential concentration, where finite-ensemble noise in quantum measurements requires exponentially many samples to extract meaningful outputs, a common issue in quantum machine learning. In this work, we go beyond static quantum machine learning tasks and address concentration in QRC for time-series processing using quantum-scrambling reservoirs. Beyond discussing how concentration effects can constrain QRC performance, we demonstrate that leveraging Hamiltonian symmetries significantly suppresses concentration, enabling robust and scalable QRC implementations. We illustrate our approach with concrete examples, including an established QRC design.