Extending echo state property for quantum reservoir computing

• URL: http://arxiv.org/abs/2403.02686v6
• Date: Fri, 19 Jul 2024 04:59:36 GMT
• Title: Extending echo state property for quantum reservoir computing
• Authors: Shumpei Kobayashi, Quoc Hoan Tran, Kohei Nakajima,
• Abstract summary: We numerically demonstrate the correspondence between non-stationary ESP in the quantum reservoir computer (QRC) framework. We also confirm the correspondence by computing linear/non-linear memory capacities that quantify input-dependent components within reservoir states. Our study presents a new understanding of the practical design of QRC and other possibly non-stationary RC systems in which non-stationary systems and subsystems are exploited.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The echo state property (ESP) represents a fundamental concept in the reservoir computing (RC) framework that ensures output-only training of reservoir networks by being agnostic to the initial states and far past inputs. However, the traditional definition of ESP does not describe possible non-stationary systems in which statistical properties evolve. To address this issue, we introduce two new categories of ESP: $\textit{non-stationary ESP}$, designed for potentially non-stationary systems, and $\textit{subspace/subset ESP}$, designed for systems whose subsystems have ESP. Following the definitions, we numerically demonstrate the correspondence between non-stationary ESP in the quantum reservoir computer (QRC) framework with typical Hamiltonian dynamics and input encoding methods using non-linear autoregressive moving-average (NARMA) tasks. We also confirm the correspondence by computing linear/non-linear memory capacities that quantify input-dependent components within reservoir states. Our study presents a new understanding of the practical design of QRC and other possibly non-stationary RC systems in which non-stationary systems and subsystems are exploited.

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