Liouvillian skin effect in quantum neural networks

TL;DR

This paper reveals that quantum neural networks can exhibit the Liouvillian skin effect, where boundary conditions significantly influence their performance, opening new avenues for exploiting this phenomenon in quantum machine learning tasks.

Contribution

It demonstrates the presence of the Liouvillian skin effect in quantum neural networks and shows how boundary conditions can be exploited to enhance quantum reservoir computing.

Findings

Boundary conditions drastically affect quantum neural network performance.

Skin effects can be utilized to improve quantum machine learning.

Performance changes are demonstrated in time-series processing tasks.

Abstract

In the field of dissipative systems, the non-Hermitian skin effect has generated significant interest due to its unexpected implications. A system is said to exhibit a skin effect if its properties are largely affected by the boundary conditions. Despite the burgeoning interest, the potential impact of this phenomenon on emerging quantum technologies remains unexplored. In this work, we address this gap by demonstrating that quantum neural networks can exhibit this behavior and that skin effects, beyond their fundamental interest, can also be exploited in computational tasks. Specifically, we show that the performance of a given complex network used as a quantum reservoir computer is dictated solely by the boundary conditions of a dissipative line within its architecture. The closure of one (edge) link is found to drastically change the performance in time-series processing, proving the possibility of exploiting skin effects for machine learning.