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Title: Complexity, action, and black holes

In an earlier paper "Complexity Equals Action" we 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.
Authors:
 [1] ;  [2] ;  [1] ;  [1] ;  [1]
  1. Stanford Univ., Stanford, CA (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Grant/Contract Number:
SC00012567; 0756174
Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 93; Journal Issue: 8; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Research Org:
Massachusetts Institute of Technology, Cambridge, MA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1248486
Alternate Identifier(s):
OSTI ID: 1247902

Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, and Zhao, Ying. Complexity, action, and black holes. United States: N. p., Web. doi:10.1103/PhysRevD.93.086006.
Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, & Zhao, Ying. Complexity, action, and black holes. United States. doi:10.1103/PhysRevD.93.086006.
Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, and Zhao, Ying. 2016. "Complexity, action, and black holes". United States. doi:10.1103/PhysRevD.93.086006. https://www.osti.gov/servlets/purl/1248486.
@article{osti_1248486,
title = {Complexity, action, and black holes},
author = {Brown, Adam R. and Roberts, Daniel A. and Susskind, Leonard and Swingle, Brian and Zhao, Ying},
abstractNote = {In an earlier paper "Complexity Equals Action" we 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.},
doi = {10.1103/PhysRevD.93.086006},
journal = {Physical Review D},
number = 8,
volume = 93,
place = {United States},
year = {2016},
month = {4}
}