Complexity, action, and black holes

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

doi:10.1103/PhysRevD.93.086006

Title: Complexity, action, and black holes

Abstract

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:

Brown, Adam R. ^[1]; Roberts, Daniel A. ^[2]; Susskind, Leonard ^[1]; Swingle, Brian ^[1]; Zhao, Ying ^[1]

Stanford Univ., Stanford, CA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: Mon Apr 18 00:00:00 EDT 2016

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1248486

Alternate Identifier(s):: OSTI ID: 1247902

Grant/Contract Number:: SC00012567; 0756174

Resource 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)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, and Zhao, Ying. Complexity, action, and black holes.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.93.086006.

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                    Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, & Zhao, Ying. Complexity, action, and black holes.  United States.  https://doi.org/10.1103/PhysRevD.93.086006

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                    Brown, Adam R., Roberts, Daniel A., Susskind, Leonard, Swingle, Brian, and Zhao, Ying. Mon .  
"Complexity, action, and black holes".  United States.  https://doi.org/10.1103/PhysRevD.93.086006.  https://www.osti.gov/servlets/purl/1248486.

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@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         = {Mon Apr 18 00:00:00 EDT 2016},

  month        = {Mon Apr 18 00:00:00 EDT 2016}

}

Copy to clipboard

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DOI: 10.1140/epjc/s10052-017-5247-1

Testing holographic conjectures of complexity with Born–Infeld black holes
journal, December 2017

Tao, Jun; Wang, Peng; Yang, Haitang
The European Physical Journal C, Vol. 77, Issue 12
DOI: 10.1140/epjc/s10052-017-5395-3

Complexity growth and shock wave geometry in AdS-Maxwell-power-Yang–Mills theory
journal, November 2018

Yaraie, Emad; Ghaffarnejad, Hossein; Farsam, Mohammad
The European Physical Journal C, Vol. 78, Issue 11
DOI: 10.1140/epjc/s10052-018-6456-y

Subregion complexity in holographic thermalization with dS boundary
journal, August 2019

Zhang, Shao-Jun
The European Physical Journal C, Vol. 79, Issue 8
DOI: 10.1140/epjc/s10052-019-7241-2

Holographic Cavalieri principle as a universal relation between holographic complexity and holographic entanglement entropy
journal, July 2018

Momeni, Davood; Faizal, Mir; Myrzakulov, Ratbay
International Journal of Modern Physics D, Vol. 27, Issue 09
DOI: 10.1142/s0218271818501031

Holographic non-computers
journal, February 2018

Barbón, José L. F.; Martín-García, Javier
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/jhep02(2018)181

Time dependence of complexity for Lovelock black holes
journal, October 2019

Fan, Zhong-Ying; Liang, Hua-Zhi
Physical Review D, Vol. 100, Issue 8
DOI: 10.1103/physrevd.100.086016

On complexity of Jackiw–Teitelboim gravity
journal, April 2019

Alishahiha, Mohsen
The European Physical Journal C, Vol. 79, Issue 4
DOI: 10.1140/epjc/s10052-019-6891-4

Investigating the holographic complexity in Einsteinian cubic gravity
journal, October 2019

Jiang, Jie; Deng, Banglin
The European Physical Journal C, Vol. 79, Issue 10
DOI: 10.1140/epjc/s10052-019-7339-6

Interface in Kerr-AdS black hole spacetime
journal, September 2019

Nagasaki, Koichi
Physical Review D, Vol. 100, Issue 6
DOI: 10.1103/physrevd.100.066032

Complexity and action for warped AdS black holes
journal, September 2018

Auzzi, Roberto; Baiguera, Stefano; Grassi, Matteo
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/jhep09(2018)013

Mixed s-sourcery: Building many-body states using bubbles of Nothing
text, January 2016

Swingle, Brian; McGreevy, John
arXiv
DOI: 10.48550/arxiv.1607.05753

Quantum Complexity and Negative Curvature
text, January 2016

Brown, Adam R.; Susskind, Leonard; Zhao, Ying
arXiv
DOI: 10.48550/arxiv.1608.02612

Thermodynamic and Holographic Information Dual to Volume
text, January 2017

Momeni, Davood; Faizal, Mir; Alsaleh, Salwa
arXiv
DOI: 10.48550/arxiv.1704.05785

Einstein's Equations from Varying Complexity
text, January 2017

Czech, Bartlomiej
arXiv
DOI: 10.48550/arxiv.1706.00965

A Complexity for Quantum Field Theory States and Application in Thermofield Double States
text, January 2017

Yang, Run-Qiu
arXiv
DOI: 10.48550/arxiv.1709.00921

Generalized Entanglement Entropies of Quantum Designs
text, January 2017

Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao
arXiv
DOI: 10.48550/arxiv.1709.04313

Holographic complexity and non-commutative gauge theory
text, January 2017

Couch, Josiah; Eccles, Stefan; Fischler, Willy
arXiv
DOI: 10.48550/arxiv.1710.07833

Evolution of Complexity Following a Global Quench
text, January 2017

Moosa, Mudassir
arXiv
DOI: 10.48550/arxiv.1711.02668

Uncomplexity and Black Hole Geometry
text, January 2017

Zhao, Ying
arXiv
DOI: 10.48550/arxiv.1711.03125

Divergences in the rate of complexification
text, January 2017

Moosa, Mudassir
arXiv
DOI: 10.48550/arxiv.1712.07137

Lovelock action with nonsmooth boundaries
text, January 2018

Cano, Pablo A.
arXiv
DOI: 10.48550/arxiv.1803.00172

Complexity Growth Rate in Lovelock Gravity
text, January 2018

Cano, Pablo A.; Hennigar, Robie A.; Marrochio, Hugo
arXiv
DOI: 10.48550/arxiv.1803.02795

Subsystem Complexity and Holography
text, January 2018

Agón, Cesar A.; Headrick, Matthew; Swingle, Brian
arXiv
DOI: 10.48550/arxiv.1804.01561

Falling Toward Charged Black Holes
text, January 2018

Brown, Adam R.; Gharibyan, Hrant; Streicher, Alexandre
arXiv
DOI: 10.48550/arxiv.1804.04156

Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
text, January 2018

An, Yu-Sen; Cai, Rong-Gen; Peng, Yuxuan
arXiv
DOI: 10.48550/arxiv.1805.07775

Effects of quintessence dark energy on the action growth and butterfly velocity
text, January 2018

Ghaffarnejad, Hossein; Farsam, Mohammad; Yaraie, Emad
arXiv
DOI: 10.48550/arxiv.1806.05735

Quantum Computation as Gravity
text, January 2018

Caputa, Pawel; Magan, Javier M.
arXiv
DOI: 10.48550/arxiv.1807.04422

Bulk geometry from entanglement entropy of CFT
text, January 2018

Saha, Ashis; Karar, Sourav; Gangopadhyay, Sunandan
arXiv
DOI: 10.48550/arxiv.1807.04646

Complexity-action of subregions with corners
text, January 2018

Caceres, Elena; Xiao, Ming-Lei
arXiv
DOI: 10.48550/arxiv.1809.09356

Holographic complexity in charged Vaidya black hole
text, January 2018

Jiang, Jie
arXiv
DOI: 10.48550/arxiv.1811.07347

On Complexity of Jackiw-Teitelboim Gravity
text, January 2018

Alishahiha, Mohsen
arXiv
DOI: 10.48550/arxiv.1811.09028

Circuit Complexity for Fermionic Thermofield Double states
text, January 2018

Jiang, Jie; Liu, Xiangjing
arXiv
DOI: 10.48550/arxiv.1812.00193

The Complexity Geometry of a Single Qubit
text, January 2019

Brown, Adam R.; Susskind, Leonard
arXiv
DOI: 10.48550/arxiv.1903.12621

Path integral optimization as circuit complexity
text, January 2019

Camargo, Hugo A.; Heller, Michal P.; Jefferson, Ro
arXiv
DOI: 10.48550/arxiv.1904.02713

Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
text, January 2019

Bhattacharya, Aranya; Grosvenor, Kevin T.; Roy, Shibaji
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DOI: 10.48550/arxiv.1905.02220

Holographic complexity of charged Taub-NUT-AdS black holes
text, January 2019

Jiang, Jie; Deng, Banglin; Li, Xiao-Wei
arXiv
DOI: 10.48550/arxiv.1908.06565

On volume subregion complexity in Vaidya spacetime
text, January 2019

Auzzi, Roberto; Nardelli, Giuseppe; Massolo, Fidel I. Schaposnik
arXiv
DOI: 10.48550/arxiv.1908.10832

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Similar Records

Title: Complexity, action, and black holes

Abstract

Citation Formats

Quantum computation vs. firewalls journal, June 2013

Time evolution of entanglement entropy from black hole interiors journal, May 2013

Computational complexity and black hole horizons: Computational complexity and black hole horizons journal, January 2016

Complexity and shock wave geometries journal, December 2014

Localized shocks journal, March 2015

Holographic complexity journal, December 2015

Holographic complexity and spacetime singularities journal, January 2016

Holographic complexity of cold hyperbolic black holes journal, November 2015

Hamiltonian complexity journal, January 2012

Ultimate physical limits to computation journal, August 2000

The world as a hologram journal, November 1995

Universal upper bound on the entropy-to-energy ratio for bounded systems journal, January 1981

Notes on spacetime thermodynamics and the observer dependence of entropy journal, March 2004

Relative entropy and the Bekenstein bound journal, September 2008

Fast scramblers journal, October 2008

Average entropy of a subsystem journal, August 1993

Black holes as mirrors: quantum information in random subsystems journal, September 2007

Towards the fast scrambling conjecture journal, April 2013

Black holes and the butterfly effect journal, March 2014

Multiple shocks journal, December 2014

Stringy effects in scrambling journal, May 2015

Geometry of quantum evolution journal, October 1990

Time in the Quantum Theory and the Uncertainty Relation for Time and Energy journal, June 1961

The maximum speed of dynamical evolution journal, September 1998

The physical limits of communication or Why any sufficiently advanced technology is indistinguishable from noise journal, October 2004

Physical Limits to Communication journal, August 2004

The speed limit of quantum unitary evolution journal, July 2004

Computational Capacity of the Universe journal, May 2002

Neutral Geometry and the Gauss-Bonnet Theorem for Two-dimensional Pseudo-Riemannian Manifolds journal, December 1992

Microscopic origin of the Bekenstein-Hawking entropy journal, June 1996

D-brane approach to black hole quantum mechanics journal, July 1996

Holographic superconductors journal, December 2008

Zero temperature limit of holographic superconductors journal, November 2009

Disrupting entanglement of black holes journal, August 2014

The gravitational shock wave of a massless particle journal, January 1985

The effect of spherical shells of matter on the Schwarzschild black hole journal, December 1985

On gravitational shock waves in curved spacetimes journal, February 1995

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory journal, September 2015

The Black Hole Singularity in AdS/CFT journal, February 2004

The typical-state paradox: diagnosing horizons with complexity: The typical-state paradox: diagnosing horizons with complexity journal, January 2016

Entanglement renormalization and holography journal, September 2012

Tensor Network States and Geometry journal, June 2011

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence journal, June 2015

Integral geometry and holography journal, October 2015

Bidirectional holographic codes and sub-AdS locality journal, January 2016

Chaos in quantum channels journal, February 2016

Charged black hole in a grand canonical ensemble journal, November 1990

Duality between electric and magnetic black holes journal, November 1995

Eternal black holes in anti-de Sitter journal, April 2003

Cool horizons for entangled black holes journal, August 2013

Quantum Computation as Geometry journal, February 2006

The information theoretic interpretation of the length of a curve journal, June 2015

Charged black hole in a grand canonical ensemble text, January 1990

Black holes as mirrors: quantum information in random subsystems text, January 2007

Relative entropy and the Bekenstein bound text, January 2008

Tensor network states and geometry text, January 2011

Towards the fast scrambling conjecture text, January 2011

Cool horizons for entangled black holes text, January 2013

Stringy effects in scrambling preprint, January 2014

Bidirectional holographic codes and sub-AdS locality text, January 2015

Chaos in quantum channels text, January 2015

Notes on Spacetime Thermodynamics and the Observer-dependence of Entropy text, January 2003

On subregion action complexity in AdS3 and in the BTZ black hole journal, January 2020

Subsystem complexity and holography journal, February 2019

Complexity growth with Lifshitz scaling and hyperscaling violation journal, July 2018

Surface counterterms and regularized holographic complexity journal, September 2017

Evolution of holographic complexity near critical point journal, September 2019

On the role of counterterms in holographic complexity journal, November 2019

On volume subregion complexity in Vaidya spacetime journal, November 2019

Quantum-First Gravity journal, February 2019

Null boundary terms for Lanczos–Lovelock gravity journal, February 2019

Quasi-topological electromagnetism: Dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality journal, December 2019

Energy cost of entanglement extraction in complex quantum systems journal, September 2018

Divergences in holographic complexity journal, April 2017

Complexity in de Sitter space journal, August 2017

Holographic complexity and thermodynamics of AdS black holes journal, July 2019

Evolutions of entanglement and complexity after a thermal quench in massive gravity theory journal, September 2019

Quantum computation vs. firewalls
journal, June 2013

Time evolution of entanglement entropy from black hole interiors
journal, May 2013

Computational complexity and black hole horizons: Computational complexity and black hole horizons
journal, January 2016

Complexity and shock wave geometries
journal, December 2014

Localized shocks
journal, March 2015

Holographic complexity
journal, December 2015

Holographic complexity and spacetime singularities
journal, January 2016

Holographic complexity of cold hyperbolic black holes
journal, November 2015

Hamiltonian complexity
journal, January 2012

Ultimate physical limits to computation
journal, August 2000

The world as a hologram
journal, November 1995

Universal upper bound on the entropy-to-energy ratio for bounded systems
journal, January 1981

Notes on spacetime thermodynamics and the observer dependence of entropy
journal, March 2004

Relative entropy and the Bekenstein bound
journal, September 2008

Fast scramblers
journal, October 2008

Average entropy of a subsystem
journal, August 1993

Black holes as mirrors: quantum information in random subsystems
journal, September 2007

Towards the fast scrambling conjecture
journal, April 2013

Black holes and the butterfly effect
journal, March 2014

Multiple shocks
journal, December 2014

Stringy effects in scrambling
journal, May 2015

Geometry of quantum evolution
journal, October 1990

Time in the Quantum Theory and the Uncertainty Relation for Time and Energy
journal, June 1961

The maximum speed of dynamical evolution
journal, September 1998

The physical limits of communication or Why any sufficiently advanced technology is indistinguishable from noise
journal, October 2004

Physical Limits to Communication
journal, August 2004

The speed limit of quantum unitary evolution
journal, July 2004

Computational Capacity of the Universe
journal, May 2002

Neutral Geometry and the Gauss-Bonnet Theorem for Two-dimensional Pseudo-Riemannian Manifolds
journal, December 1992

Microscopic origin of the Bekenstein-Hawking entropy
journal, June 1996

D-brane approach to black hole quantum mechanics
journal, July 1996

Holographic superconductors
journal, December 2008

Zero temperature limit of holographic superconductors
journal, November 2009

Disrupting entanglement of black holes
journal, August 2014

The gravitational shock wave of a massless particle
journal, January 1985

The effect of spherical shells of matter on the Schwarzschild black hole
journal, December 1985

On gravitational shock waves in curved spacetimes
journal, February 1995

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
journal, September 2015

The Black Hole Singularity in AdS/CFT
journal, February 2004

The typical-state paradox: diagnosing horizons with complexity: The typical-state paradox: diagnosing horizons with complexity
journal, January 2016

Entanglement renormalization and holography
journal, September 2012

Tensor Network States and Geometry
journal, June 2011

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

Integral geometry and holography
journal, October 2015

Bidirectional holographic codes and sub-AdS locality
journal, January 2016

Chaos in quantum channels
journal, February 2016

Charged black hole in a grand canonical ensemble
journal, November 1990

Duality between electric and magnetic black holes
journal, November 1995

Eternal black holes in anti-de Sitter
journal, April 2003

Cool horizons for entangled black holes
journal, August 2013

Quantum Computation as Geometry
journal, February 2006

The information theoretic interpretation of the length of a curve
journal, June 2015

Charged black hole in a grand canonical ensemble
text, January 1990

Black holes as mirrors: quantum information in random subsystems
text, January 2007

Relative entropy and the Bekenstein bound
text, January 2008

Tensor network states and geometry
text, January 2011

Towards the fast scrambling conjecture
text, January 2011

Cool horizons for entangled black holes
text, January 2013

Stringy effects in scrambling
preprint, January 2014

Bidirectional holographic codes and sub-AdS locality
text, January 2015

Chaos in quantum channels
text, January 2015

Notes on Spacetime Thermodynamics and the Observer-dependence of Entropy
text, January 2003

On subregion action complexity in AdS3 and in the BTZ black hole
journal, January 2020

Subsystem complexity and holography
journal, February 2019

Complexity growth with Lifshitz scaling and hyperscaling violation
journal, July 2018

Surface counterterms and regularized holographic complexity
journal, September 2017

Evolution of holographic complexity near critical point
journal, September 2019

On the role of counterterms in holographic complexity
journal, November 2019

On volume subregion complexity in Vaidya spacetime
journal, November 2019

Quantum-First Gravity
journal, February 2019

Null boundary terms for Lanczos–Lovelock gravity
journal, February 2019

Quasi-topological electromagnetism: Dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality
journal, December 2019

Energy cost of entanglement extraction in complex quantum systems
journal, September 2018

Divergences in holographic complexity
journal, April 2017

Complexity in de Sitter space
journal, August 2017

Holographic complexity and thermodynamics of AdS black holes
journal, July 2019

Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
journal, September 2019

Holographic complexity of charged Taub-NUT-AdS black holes
journal, September 2019

Operator approach to complexity: Excited states
journal, September 2019

Adjusted complexity equals action conjecture
journal, September 2019