Holographic Spacetimes as Quantum Circuits of Path-Integrations

TL;DR

This paper proposes a novel view of holographic spacetimes as collections of quantum circuits constructed via path-integrals, offering new insights into holographic duality, complexity, and the emergence of gravity from quantum information.

Contribution

It introduces a framework relating gravity dual surfaces to quantum circuits through path-integrals, generalizing surface/state duality and deriving holographic complexity formulas.

Findings

Holographic spacetimes can be modeled as quantum circuits via path-integrals.

Derived a new formula relating quantum gate counts to surface areas.

Provided a heuristic explanation for gravity emerging from quantum circuits.

Abstract

We propose that holographic spacetimes can be regarded as collections of quantum circuits based on path-integrals. We relate a codimension one surface in a gravity dual to a quantum circuit given by a path-integration on that surface with an appropriate UV cut off. Our proposal naturally generalizes the conjectured duality between the AdS/CFT and tensor networks. This largely strengthens the surface/state duality and also provides a holographic explanation of path-integral optimizations. For static gravity duals, our new framework provides a derivation of the holographic complexity formula given by the gravity action on the WDW patch. We also propose a new formula which relates numbers of quantum gates to surface areas, even including time-like surfaces, as a generalization of the holographic entanglement entropy formula. We argue the time component of the metric in AdS emerges from the density of unitary quantum gates in the dual CFT. Our proposal also provides a heuristic understanding how the gravitational force emerges from quantum circuits.