Dynamical learning and quantum memory with non-Hermitian many-body systems

TL;DR

This paper explores how non-Hermitian many-body systems can serve as dynamic resources for quantum memory and learning, revealing a spectral transition that controls their computational capacity and memory features.

Contribution

It demonstrates the link between spectral transitions in non-Hermitian systems and their ability to perform quantum learning and memory tasks, introducing tunable control over these properties.

Findings

Spectral transition at the exceptional point affects learning capacity.

Disorder and interaction strength control the learnability threshold.

Non-Hermitian systems can support reservoir computing for quantum memory.

Abstract

Non-Hermitian (NH) systems provide a fertile platform for quantum technologies, owing in part to their distinct dynamical phases. These systems can be characterized by the preservation or spontaneous breaking of parity-time reversal symmetry, significantly impacting the dynamical behavior of quantum resources such as entanglement and purity; resources which in turn govern the system's information processing and memory capacity. Here we investigate this relationship using the example of an interacting NH spin system defined on random graphs. We show that the onset of the first exceptional point - marking the real-to-complex spectral transition - also corresponds to an abrupt change in the system's learning capacity. We further demonstrate that this transition is controllable via local disorder and spin interactions strength, thereby defining a tunable learnability threshold. Within the learning phase, the system exhibits the key features required for memory-dependent reservoir computing. This makes explicit a direct link between spectral structure and computational capacity, further establishing non-Hermiticity, and more broadly engineered dissipation, as a dynamic resource for temporal quantum machine learning.