发表机构
School of Physics, Sun Yat-sen University; School of Electronics and Information Technology, Sun Yat-sen University; State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University; Department of Physics, Hunan Normal University（中山大学物理学院; 中山大学电子与信息工程学院; 中山大学光电信息材料与技术国家重点实验室; 湖南师范大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立微观响应-性能框架，将Liouvillian动力学与量子储层计算任务性能直接关联，揭示输入生成、读出可见、目标相关及可分辨性条件，并证明弱测量和延迟反馈可激活或引导任务相关信息流以提升性能。
AI 中文摘要
开放量子系统为量子储层计算中的时间信息处理提供了物理基础，然而将其动力学与计算性能联系起来的微观机制仍不清楚。在此，我们建立了一个微观的响应-性能框架，将Liouvillian动力学直接与任务性能联系起来。我们将可观测的Volterra权重分解为$W^{(q)}=BH^{(q)}$，将内部输入历史路径与其读出可见性分离，并证明只有当动力学响应是输入生成的、读出可见的、目标相关的且可分辨于正则化尺度之上时，它才对任务有所贡献。该框架揭示了Liouvillian模式如何控制任务相关信息的保留和传播，而对称性决定了哪些分量对读出保持可见。它进一步确立了不同的协方差模式如何编码不同的时间信息结构，以及系统参数和处理协议如何重塑其贡献以提升QRC性能。热化驱动储层从保留输入历史的处理过程转变为由最近输入主导的响应，随后正则化抑制残余信息。我们最终证明，弱测量可以通过解除对称性强加的通道等价性来激活任务相关的协方差模式，而延迟反馈为历史信息创建受控的返回路径。这些结果建立了开放系统动力学与计算性能之间的微观联系，为在量子储层中工程设计任务相关信息流提供了原理。
英文摘要
Open quantum systems offer a physical substrate for temporal information processing in quantum reservoir computing, yet the microscopic mechanisms linking their dynamics to computational performance remain unclear. Here we establish a microscopic response-to-performance framework that connects Liouvillian dynamics directly to task performance. We decompose observable Volterra weights as $W^{(q)}=BH^{(q)}$, separating internal input-history pathways from their readout visibility, and show that a dynamical response contributes to a task only if it is input-generated, readout-visible, target-correlated, and resolvable above the regularization scale. This framework reveals how Liouvillian modes govern the retention and propagation of task-relevant information, while symmetries determine which components remain visible to the readout. It further establishes how distinct covariance modes encode different temporal information structures and how system parameters and processing protocols can reshape their contributions to improve QRC performance. Thermalization drives the reservoir from processing that retains input history to a response dominated by the most recent input before regularization suppresses the residual information. We finally show that weak measurement can activate task-relevant covariance modes by lifting symmetry-imposed channel equivalence, whereas delayed feedback creates controlled return pathways for historical information. These results establish a microscopic connection between open-system dynamics and computational performance, providing principles for engineering task-relevant information flow in quantum reservoirs.
Comments43 pages, 11 figures, comments welcome
