A Single Atom in Front of a Mirror is a Universal Reservoir Computer

2026-08-10

AI Summary

This study addresses the realization of universal approximation capability in reservoir computing within an extremely minimal physical system. The authors propose a minimal quantum reservoir composed of a single atom coupled to a mirror and demonstrate that, in the linear transducer limit, arbitrary-precision approximation of nonlinear mappings with fading memory can be achieved by appropriately tuning the measurement configuration. This work establishes, for the first time, that a single quantum system alone suffices to fulfill the universality requirement of reservoir computing, thereby transcending the conventional paradigm reliant on complex network architectures. Theoretical analysis quantifies the physical resources and number of modes required to attain a target accuracy, and empirical evaluations on real-world tasks show performance comparable to classical baseline models, confirming the effective computational power of this minimalist quantum device.

Abstract

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

Problem

• reservoir computing
• universal approximation
• single atom
• fading-memory maps
• quantum reservoir

Innovation

• reservoir computing
• universal approximation
• single-atom system
• fading-memory maps
• quantum reservoir