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Quantum Complexity and Negative Curvature

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

Aug 8, 2016

19 pages

Published in:

Phys.Rev.D 95 (2017) 4, 045010

Published: Feb 22, 2017

e-Print:

1608.02612 [hep-th]

DOI:

10.1103/PhysRevD.95.045010

View in:

reference search164 citations

Citations per year

Abstract: (APS)

As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system—classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.

Note:

43 pages

dimension: 2
curvature
strong coupling
Hamiltonian
geometry

References(24)

Figures(19)

[1]

Computational Complexity and Black Hole Horizons

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

- Fortsch.Phys. 64 (2016) 44-48 (addendum),
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•
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•
DOI:
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[2]

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.
)

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•
e-Print:
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•
DOI:
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[3]

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

- JHEP 03 (2015) 051
•
e-Print:
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•
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Michael A. Nielsen
(
- Queensland U.
)

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•
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(
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)
,
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(
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)

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•
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(
- Yale U.
)
,
Jinwu Ye
(
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)

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

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•
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•
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[12]

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.
)

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•
e-Print:
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•
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[13]

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.
)

- Phys.Rev.D 93 (2016) 8, 086006
•
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•
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[14]

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S.W. Hawking
(
- Cambridge U.
)
,
Don N. Page
(
- Penn State U.
)

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- JHEP 08 (2016) 106
•
e-Print:
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•
DOI:
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[16]

unpublished

A. Kitaev

[17]

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

- JHEP 09 (2007) 120
•
e-Print:
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•
DOI:
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[18]

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•
e-Print:
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•
DOI:
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[19]

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Stephen H. Shenker
(
)
,
Douglas Stanford
(
)

- JHEP 03 (2014) 067
•
e-Print:
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•
DOI:
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[20]

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

[21]

Stringy effects in scrambling

Stephen H. Shenker
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Douglas Stanford
(
)

- JHEP 05 (2015) 132
•
e-Print:
- 1412.6087
•
DOI:
- 10.1007/JHEP05(2015)132

[22]

unpublished

L. Susskind
,
Y. Zhao

[23]

Multiple Shocks

Stephen H. Shenker
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Douglas Stanford
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

- JHEP 12 (2014) 046
•
e-Print:
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•
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[24]

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Seth Lloyd

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•
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