Computational Complexity in Analogue Gravity

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.