Talk 135 - Spectral properties of the sparse SYK model, with analysis of recent experimental simulation of holography

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a simple toy model of holography that has seen widespread study in the area of quantum gravity. It is particularly notable for its feasibility of simulation on near-term quantum devices. Recently, Swingle et al. introduced a sparsified version of the SYK model and analyzed its holographic properties, which are remarkably robust to deletion of Majorana interaction terms. Here we analyze its spectral and quantum chaotic properties as they pertain to holography as well as how they scale with sparsity and system size through large scale numerics. We identify at least two transition points at which features of chaos and holography are lost as the model is sparsified, and above which all important features are preserved, which may serve as guidelines for future experiments to simulate quantum gravity. Additionally, we apply these analyses to the SYK model that was recently experimentally simulated on the Google Sycamore quantum processor, which itself was a highly sparsified SYK model obtained through a machine learning algorithm incorporating mutual information signatures of a traversable wormhole.