Holographic spacetimes as quantum circuits of path-integrations

• Takayanagi, Tadashi

  Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University･Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo

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.

Journal

• Journal of High Energy Physics

  Journal of High Energy Physics 2018 048-, 2018-12

  Springer Nature

Keywords

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

Details

• CRID: 1050001338209197568
• NII Article ID: 120006551751
• ISSN: 10298479
• DOI: 10.1007/jhep12(2018)048
• HANDLE: 2433/236104
• Web Site: https://link.springer.com/content/pdf/10.1007/JHEP12(2018)048.pdf
• Web Site: https://link.springer.com/article/10.1007/JHEP12(2018)048/fulltext.html
• Text Lang: en
• Article Type: journal article
• Data Source:
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  • CiNii Articles
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