发表机构
The University of Tokyo; Donostia International Physics Center; Saitama University; University of Turku; Turku Collegium for Science, Medicine and Technology, University of Turku; Technische Universitat Ilmenau（东京大学; 圣塞巴斯蒂安国际物理中心; 埼玉大学; 图尔库大学; 图尔库大学科学、医学与技术学院; 伊尔梅瑙工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文阐明噪声对信息处理能力的影响，提出正交投影协方差重构（CROP）方法，从含噪观测中直接重构无噪声IPC，并在经典与量子储层中验证其优于系综平均。研究为恢复含噪物理系统的计算结构提供通用途径。
AI 中文摘要
驱动动力系统在瞬态编码过去输入的复杂变换时能够进行计算。信息处理能力（IPC）框架允许对这些计算特性进行详细核算，然而其在含噪系统中的解释仍不完整。在本工作中，我们阐明了噪声如何影响IPC以及如何重构无噪声的IPC。首先，我们展示了如何区分未受扰动系统的动力学与随机动力学的无噪声分量：对噪声实现进行平均的响应所测得的IPC通常与未受扰动系统的IPC不同。我们明确证明了噪声可以重新分配计算能力，有时甚至能增强特定任务上的性能，而不仅仅是降低固定计算的质量。随后，我们引入了正交投影协方差重构（CROP）方法，该方法直接从含噪观测中重构无噪声分量的协方差和IPC，无需系统或噪声的详细模型。在固定的总测量预算下，对经典非线性储层的数值测试表明，CROP估计无噪声IPC比重复试验的系综平均这一标准做法更准确。我们在遭受不可避免的测量噪声的量子储层中发现了同样的优势。我们的结果为从有限观测中恢复含噪物理系统的计算结构提供了一条通用途径。
英文摘要
Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. In this work, we clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, we show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. We explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. We then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. We find the same advantage in a quantum reservoir subject to unavoidable measurement noise. Our results provide a general route to recovering the computational structure of noisy physical systems from finite observations.
