Complexity, action, and black holes - INSPIRE

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Complexity, action, and black holes

Adam R. Brown
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, CTP and
- MIT, Cambridge, Dept. Phys.
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Brian Swingle
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

Dec 15, 2015

32 pages

Published in:

Phys.Rev.D 93 (2016) 8, 086006

Published: Apr 18, 2016

e-Print:

1512.04993 [hep-th]

DOI:

10.1103/PhysRevD.93.086006

View in:

reference search669 citations

Citations per year

Abstract: (APS)

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.

Note:

55+14 pages, many figures. v2: (so many) typos fixed, references added

black hole
holography
computer
network

References(72)

Figures(20)

[1]

Holographic Complexity Equals Bulk Action?

Adam R. Brown
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, CTP and
- MIT, LNS
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Brian Swingle
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.Lett. 116 (2016) 19, 191301
•
e-Print:
- 1509.07876
•
DOI:
- 10.1103/PhysRevLett.116.191301

[2]

Quantum Computation vs. Firewalls

Daniel Harlow
(
- Princeton U., CTP
)
,
Patrick Hayden
(
- McGill U.
)

- JHEP 06 (2013) 085
•
e-Print:
- 1301.4504
•
DOI:
- 10.1007/JHEP06(2013)085

[3]

Time Evolution of Entanglement Entropy from Black Hole Interiors

- JHEP 05 (2013) 014
•
e-Print:
- 1303.1080
•
DOI:
- 10.1007/JHEP05(2013)014

[5]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[5]

Computational Complexity and Black Hole Horizons

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
- Fortsch.Phys. 64 (2016) 24-43
•
e-Print:
- 1403.5695
•
DOI:
- 10.1002/prop.201500092

[6]

Complexity and Shock Wave Geometries

Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- Phys.Rev.D 90 (2014) 12, 126007
•
e-Print:
- 1406.2678
•
DOI:
- 10.1103/PhysRevD.90.126007

[7]

Localized shocks

Daniel A. Roberts
(
- MIT, Cambridge, CTP
)
,
Douglas Stanford
(
)
,
Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- JHEP 03 (2015) 051
•
e-Print:
- 1409.8180
•
DOI:
- 10.1007/JHEP03(2015)051

[8]

Switchbacks and the Bridge to Nowhere

Leonard Susskind
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Ying Zhao
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

e-Print:
- 1408.2823

[9]

Holographic Complexity

Mohsen Alishahiha
(
- IPM, Tehran
)

- Phys.Rev.D 92 (2015) 12, 126009
•
e-Print:
- 1509.06614
•
DOI:
- 10.1103/PhysRevD.92.126009

[10]

Holographic complexity and spacetime singularities

Jose L.F. Barbon
(
- Madrid, IFT
)
,
Eliezer Rabinovici
(
- Paris, LPTHE and
- Hebrew U.
)

- JHEP 01 (2016) 084
•
e-Print:
- 1509.09291
•
DOI:
- 10.1007/JHEP01(2016)084

[11]

Holographic Complexity Of Cold Hyperbolic Black Holes

Jose L. F. Barbon
(
- Madrid, IFT
)
,
Javier Martin-Garcia
(
- Madrid, IFT
)

- JHEP 11 (2015) 181
•
e-Print:
- 1510.00349
•
DOI:
- 10.1007/JHEP11(2015)181

[12]

Hamiltonian complexity

Tobias J. Osborne

- Rept.Prog.Phys. 75 (2012) 2, 022001
•
DOI:
- 10.1088/0034-4885/75/2/022001

[13]

Quantum Hamiltonian Complexity

S. Gharibian
,
Y. Huang
,
Z. Landau
,
S.W. Shin

•
e-Print:
- 1401.3916

[14]

Ultimate physical limits to computation

Seth Lloyd

- Nature 406 (2000) 1047-1054
•
DOI:
- 10.1038/35023282

[15]

Bulk and Transhorizon Measurements in AdS/CFT

Idse Heemskerk
(
- UC, Santa Barbara
)
,
Donald Marolf
(
- UC, Santa Barbara and
- Santa Barbara, KITP
)
,
Joseph Polchinski
(
- UC, Santa Barbara and
- Santa Barbara, KITP
)
,
James Sully
(
- UC, Santa Barbara
)

- JHEP 10 (2012) 165
•
e-Print:
- 1201.3664
•
DOI:
- 10.1007/JHEP10(2012)165

[16]

Dimensional reduction in quantum gravity

Gerard 't Hooft
(
- Utrecht U.
)

- Conf.Proc.C 930308 (1993) 284-296
•
e-Print:
- gr-qc/9310026

[17]

The World as a hologram

Leonard Susskind
(
- Stanford U., Phys. Dept.
)

- J.Math.Phys. 36 (1995) 6377-6396
•
e-Print:
- hep-th/9409089
•
DOI:
- 10.1063/1.531249

[18]

A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems

Jacob D. Bekenstein
(
- Santa Barbara, KITP
)

- Phys.Rev.D 23 (1981) 287
•
DOI:
- 10.1103/PhysRevD.23.287

[19]

Notes on space-time thermodynamics and the observer dependence of entropy

Donald Marolf
(
- UC, Santa Barbara
)
,
Djordje Minic
(
- Virginia Tech.
)
,
Simon F. Ross
(
- Durham U., Dept. of Math.
)

- Phys.Rev.D 69 (2004) 064006
•
e-Print:
- hep-th/0310022
•
DOI:
- 10.1103/PhysRevD.69.064006

[20]

Relative entropy and the Bekenstein bound

H. Casini
(
- Centro Atomico Bariloche
)

- Class.Quant.Grav. 25 (2008) 205021
•
e-Print:
- 0804.2182
•
DOI:
- 10.1088/0264-9381/25/20/205021

[21]

Fast Scramblers

- JHEP 10 (2008) 065
•
e-Print:
- 0808.2096
•
DOI:
- 10.1088/1126-6708/2008/10/065

[22]

Average entropy of a subsystem

Don N. Page
(
- Alberta U.
)

- Phys.Rev.Lett. 71 (1993) 1291-1294
•
e-Print:
- gr-qc/9305007
•
DOI:
- 10.1103/PhysRevLett.71.1291

[23]

Black holes as mirrors: Quantum information in random subsystems

Patrick Hayden
(
- McGill U.
)
,
John Preskill
(
- Caltech, IQI
)

- JHEP 09 (2007) 120
•
e-Print:
- 0708.4025
•
DOI:
- 10.1088/1126-6708/2007/09/120

[24]

A bound on chaos

- JHEP 08 (2016) 106
•
e-Print:
- 1503.01409
•
DOI:
- 10.1007/JHEP08(2016)106

[25]

Towards the Fast Scrambling Conjecture

Nima Lashkari
(
- McGill U.
)
,
Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Matthew Hastings
(
- Duke U. and
- Station Q, UCSB
)
,
Tobias Osborne
(
- Leibniz U., Hannover and
- Hannover U.
)
,
Patrick Hayden
(
- McGill U. and
- Perimeter Inst. Theor. Phys.
)

- JHEP 04 (2013) 022
•
e-Print:
- 1111.6580
•
DOI:
- 10.1007/JHEP04(2013)022

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