Computational Complexity in Analogue Gravity

TL;DR

This paper explores the concept of computational complexity within analogue gravity systems, linking it to the Lloyd bound and fluid/gravity duality, and proposes experimental tests for these theoretical ideas.

Contribution

It introduces an interpretation of computational complexity in condensed matter systems and connects the Lloyd bound to the KSS bound in fluid/gravity duality.

Findings

Lloyd bound is roughly equivalent to the KSS bound in fluid/gravity duality.

Provides experimental criteria to test the Lloyd bound in laboratories.

Establishes a link between complexity, uncertainty principle, and gravity analogies.

Abstract

Analogue gravity helps to find some gravitational systems which are similar to the evolution of perturbation in condensed matter systems. These analogies provide a very good tool for either side. In other words, some aspects of gravity could be simulated in condensed matter laboratories. In this study, we are going to find an interpretation for computational complexity in condensed matter systems and the analogue of the uncertainty principle as the Lloyd bound. We show that this inequality roughly is equivalent to the KSS bound in the fluid/gravity duality and provides some experimental criteria to test the Lloyd bound in the laboratory.