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Journal of High Energy Physics

, 2018:48 | Cite as

Holographic spacetimes as quantum circuits of path-integrations

  • Tadashi TakayanagiEmail author
Open Access
Regular Article - Theoretical Physics

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.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP)Kyoto UniversityKyotoJapan
  2. 2.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan

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