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Spacetime as a quantum circuit

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  • Published: 21 April 2021
  • Volume 2021, article number 207, (2021)
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Spacetime as a quantum circuit
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  • A. Ramesh Chandra1,
  • Jan de Boer1,
  • Mario Flory2,3,
  • Michal P. Heller4,
  • Sergio Hörtner1 &
  • …
  • Andrew Rolph  ORCID: orcid.org/0000-0002-8014-95471 

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A preprint version of the article is available at arXiv.

Abstract

We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic \( T\overline{T} \), we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Amsterdam, PO Box 94485, 1090 GL, Amsterdam, The Netherlands

    A. Ramesh Chandra, Jan de Boer, Sergio Hörtner & Andrew Rolph

  2. Institute of Physics, Jagiellonian University, 30-348, Kraków, Poland

    Mario Flory

  3. Instituto de Física Téorica IFT-UAM/CSIC, Universidad Autonoma de Madrid, 28049, Madrid, Spain

    Mario Flory

  4. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476, Potsdam-Golm, Germany

    Michal P. Heller

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  1. A. Ramesh Chandra
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ArXiv ePrint: 2101.01185

On leave of absence from: National Centre for Nuclear Research, 02-093 Warsaw, Poland (Michal P. Heller)

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Chandra, A.R., de Boer, J., Flory, M. et al. Spacetime as a quantum circuit. J. High Energ. Phys. 2021, 207 (2021). https://doi.org/10.1007/JHEP04(2021)207

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  • Received: 23 January 2021

  • Accepted: 30 March 2021

  • Published: 21 April 2021

  • DOI: https://doi.org/10.1007/JHEP04(2021)207

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Keywords

  • AdS-CFT Correspondence
  • Gauge-gravity correspondence
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