Efficiently and Reliably Measuring Information Processing Capacity in Dynamical Systems via Kernels

2026-10-02

AI Summary

This study addresses the combinatorial explosion in computational complexity when calculating information processing capacity (IPC) as polynomial order increases. To overcome this, we propose the Kernel-IPC framework, which leverages the kernel trick to implicitly map the complete basis function space. This enables exact IPC evaluation over infinite-dimensional bases without explicit enumeration or truncation, fundamentally eliminating truncation errors while significantly reducing computational costs. Furthermore, statistical hypothesis testing is incorporated to rigorously compare system performance. Experimental validation on echo state networks and disordered spin chains confirms the effectiveness of the proposed framework. Ultimately, this work establishes a reliable and efficient paradigm for evaluating quantum reservoir computing systems.

Abstract

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.

Problem

• Information Processing Capacity
• Dynamical Systems
• Computational Complexity
• Reservoir Computing

Innovation

• Information Processing Capacity
• Kernel methods
• Dynamical systems
• Reservoir computing
• Null-hypothesis test