Hamiltonian-Driven Architectures for Non-Markovian Quantum Reservoir Computing

TL;DR

This paper introduces a Hamiltonian-based framework for non-Markovian quantum reservoir computing, demonstrating that strong non-Markovian effects can violate the echo-state property and improve performance on complex tasks.

Contribution

It presents the first quantum reservoir computing architecture that leverages non-Markovian dynamics to enhance memory and computational capabilities.

Findings

Non-Markovian regimes slow memory decay compared to Markovian.

Non-Markovian dynamics violate the echo-state property.

Enhanced performance on nonlinear autoregressive moving-average tasks.

Abstract

We propose a Hamiltonian-level framework for non-Markovian quantum reservoir computing directly tailored for analog hardware implementations. By dividing the reservoir into a system block and an environment block and evolving their joint state under a unified Hamiltonian, our architecture naturally embeds memory backflow by harnessing entanglement-induced information backflow with tunable coupling strengths. Numerical benchmarks on short-term memory tasks demonstrate that operating in non-Markovian regimes yields significantly slower memory decay compared to the Markovian limit. Further analyzing the echo-state property (ESP), showing that the non-Markovian quantum reservoir evolves from two different initial states, they do not converge to the same trajectory even after a long time, strongly suggesting that the ESP is effectively violated. Our work provides the first demonstration in quantum reservoir computing that strong non-Markovianity can fundamentally violate the ESP, such that conventional linear-regression readouts fail to deliver stable training and inference. Finally, we experimentally showed that, with an appropriate time-evolution step size, the non-Markovian reservoir exhibits superior performance on higher-order nonlinear autoregressive moving-average(NARMA) tasks.