Complexity, action, and black holes

Adam R. Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, and Ying Zhao

Phys. Rev. D 93, 086006 – Published 18 April 2016

Abstract

Our earlier paper “Complexity Equals Action” conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the “Wheeler-DeWitt” patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.

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Received 31 January 2016

DOI:https://doi.org/10.1103/PhysRevD.93.086006

Physics Subject Headings (PhySH)

Gauge-gravity dualities Quantum aspects of black holes Quantum information processing

Computational complexity

Particles & Fields

Authors & Affiliations

Adam R. Brown¹, Daniel A. Roberts², Leonard Susskind¹, Brian Swingle¹, and Ying Zhao¹

¹Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA
²Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

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Issue

Vol. 93, Iss. 8 — 15 April 2016

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Physical Review D

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