Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments

TL;DR

This paper presents an interpretable neural network model that reconstructs higher-dimensional gravity metrics from condensed matter data, advancing the practical application of AdS/CFT correspondence in tabletop quantum gravity experiments.

Contribution

The paper introduces a novel neural network with a Runge-Kutta layer for bulk reconstruction, enabling emergent gravity metrics from linear response data.

Findings

Neural network successfully reconstructs gravity metrics from data.

Model demonstrates interpretability of emergent spacetime.

Applicable to future tabletop quantum gravity experiments.

Abstract

We introduce a novel interpretable Neural Network (NN) model designed to perform precision bulk reconstruction under the AdS/CFT correspondence. According to the correspondence, a specific condensed matter system on a ring is holographically equivalent to a gravitational system on a bulk disk, through which tabletop quantum gravity experiments may be possible as reported in arXiv:2211.13863. The purpose of this paper is to reconstruct a higher-dimensional gravity metric from the condensed matter system data via machine learning using the NN. Our machine reads spatially and temporarily inhomogeneous linear response data of the condensed matter system, and incorporates a novel layer that implements the Runge-Kutta method to achieve better numerical control. We confirm that our machine can let a higher-dimensional gravity metric be automatically emergent as its interpretable weights, using a linear response of the condensed matter system as data, through supervised machine learning. The developed method could serve as a foundation for generic bulk reconstruction, i.e., a practical solution to the AdS/CFT correspondence, and would be implemented in future tabletop quantum gravity experiments.