Spacetime as the optimal generative network of quantum states: a roadmap to QM=GR?

TL;DR

This paper proposes a novel framework where spacetime geometry emerges as an optimal generative network of quantum states, linking quantum complexity with gravitational structure through tensor networks inspired by deep learning.

Contribution

It introduces a mechanism connecting quantum state complexity with spacetime geometry, providing a constructive and dynamic model aligned with the QM=GR hypothesis.

Findings

Spacetime geometry can be modeled as a geodesic tensor network.

The model naturally incorporates QEC-like structures seen in AdS/CFT.

A potential derivation of gravity equations from quantum state complexity.

Abstract

The idea that spacetime geometry is built from quantum entanglement has been widely accepted in the last years. But how exactly the geometry is related with quantum states is still unclear. In this note, based on the idea of deep learning, we propose a mechanism for Susskind's QM=GR hypothesis, spacetime geometry as the optimal generative network of quantum states. We speculate that the space geometry stems as a geodesic tensor network which defines the quantum state complexity of a fundamental quantum state under a given metric. Spacetime corresponds to an evolving tensor network that generates an evolutional fundamental quantum system. This mechanism provides (a) a constructive correspondence between quantum states and spacetime geometry; (b)a spacetime structure emerging from a highly constrained geodesic so that the QEC-like structure shown in AdS/CFT can be naturally realized and (c) a mechanism to derive the gravity equation from the concept of quantum state complexity. With this mechanism, spacetime can have a quantum mechanical description. We hope this may lead to another view direction to understand the basic rules of our world.