发表机构
School of Computer Science and Statistics, Trinity College Dublin; Trinity Quantum Alliance; School of Physics; Trinity College Dublin（都柏林三一学院计算机科学与统计学院; 三一量子联盟; 物理学院; 都柏林三一学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出核信息处理容量（KIPC）框架，利用核方法高效计算动力系统的总信息处理容量，避免基函数枚举和阶数截断，并验证其在回声状态网络和量子储层计算中的有效性。
AI 中文摘要
信息处理容量（IPC）是一种强大的系统无关指标，用于量化动力系统的计算能力，并广泛应用于量子储层计算。然而，标准IPC存在严重的计算限制。计算IPC涉及估计系统通过线性回归重构（原则上）无限族的延迟输入的正交多项式函数的能力。在实践中，这种评估必须是有界的，因此我们只需考虑最高达到选定最大阶数的多项式。此外，计算IPC的计算复杂度随所考虑的最大阶数和延迟呈组合增长。在这里，我们引入了核信息处理容量（KIPC），这是一种可扩展的框架，利用核方法计算总IPC，而无需显式枚举基函数。这使我们能够考虑完整的（无限）基（无需截断阶数）。我们还提供了一种零假设检验，用于统计比较两个动力系统的KIPC。我们在回声状态网络上验证了KIPC，并展示了其在无序自旋链上用于量子储层计算的实用性。
英文摘要
Information Processing Capacity (IPC) is a powerful system-agnostic metric for quantifying a dynamical system's computational capability and is widely used in quantum reservoir computing. However, standard IPC suffers from severe computational limitations. Computing IPC involves estimating how well the system can reconstruct, via linear regression, an (in principle) infinite family of orthogonal polynomial functions of delayed inputs. In practice, this evaluation must be made finite, so we need only to consider polynomials up to a chosen maximum degree. Moreover, the computational complexity for computing IPC grows combinatorially with the considered maximum degree and delay. Here, we introduce Kernel-IPC (KIPC), a scalable framework that uses kernel methods to compute the total IPC without explicitly enumerating basis functions. This allows us to account for the full (infinite) basis (without degree truncation). We also provide a null-hypothesis test for statistically comparing the KIPC of two dynamical systems. We validate KIPC on an echo state network and demonstrate its utility for quantum reservoir computing on a disordered spin chain.
