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.

翻译：回声状态属性（ESP）是储层计算（RC）框架中的一个基本概念，它通过忽略初始状态和遥远的过去输入，确保仅需对储层网络进行输出端训练。然而，传统ESP定义无法描述统计特性可能演化的非平稳系统。为解决这一问题，我们引入两类新的ESP：针对潜在非平稳系统的\textit{非平稳ESP}，以及针对子系统具备ESP的系统的\textit{子空间/子集ESP}。基于这些定义，我们通过非线性自回归滑动平均（NARMA）任务，从数值上演示了具有典型哈密顿动力学和输入编码方法的量子储层计算机（QRC）框架中非平稳ESP的一致性。此外，我们通过计算用于量化储层状态中输入相关成分的线性/非线性记忆能力，进一步验证了这种对应关系。本研究为QRC及其他潜在非平稳RC系统的实际设计提供了新视角，其中非平稳系统及子系统得以充分利用。