Quantum Wiener architecture for quantum reservoir computing

TL;DR

This paper introduces quantum Wiener architectures for quantum reservoir computing, proving their theoretical properties and demonstrating superior empirical performance over classical and quantum models.

Contribution

It provides the first rigorous proof of fading-memory and universality for qWiener systems and develops a kernel-theoretic framework for their analysis.

Findings

qWiener systems retain fading-memory and universality.

qWiener reservoirs induce deep kernels for expressiveness.

Empirical results show performance gains over prior models.

Abstract

This work focuses on quantum reservoir computing and, in particular, on quantum Wiener architectures (qWiener), consisting of quantum linear dynamic networks with weak continuous measurements and classical nonlinear static readouts. We provide the first rigorous proof that qWiener systems retain the fading-memory property and universality of classical Wiener architectures, despite quantum constraints on linear dynamics and measurement back-action. Furthermore, we develop a kernel-theoretic interpretation showing that qWiener reservoirs naturally induce deep kernels, providing a principled framework for analysing their expressiveness. We further characterise the simplest qWiener instantiation, consisting of concatenated quantum harmonic oscillators, and show the difference with respect to the classical case. Finally, we empirically evaluate the architecture on standard reservoir computing benchmarks, demonstrating systematic performance gains over prior classical and quantum reservoir computing models.