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Conjecture in quantum gravity
In
quantum gravity and
quantum complexity theory , the complexity equals action duality (CA-duality ) is the
conjecture that the
gravitational action of any
semiclassical state with an asymptotically
anti-de Sitter background corresponds to quantum computational complexity, and that black holes produce complexity at the fastest possible rate.
[1] In technical terms, the complexity of a
quantum state on a spacelike slice of the
conformal field theory dual is proportional to the
action of the
Wheeler–DeWitt patch (WDW patch) of that spacelike slice in the bulk. The WDW patch is the union of all possible spacelike slices of the bulk with the CFT slice as its boundary.
[2]
[3]
[4]
This conjecture has been tested against several
anti-de Sitter
black hole backgrounds with and without
shock waves , and was found to pass all the tests.
[3] The action for the WDW patch of a wormhole grows linearly in time for an exponentially long period. Dually, quantum circuit complexity has also been shown to grow linearly for an exponentially long time
[5]
References
^ Hartman, Thomas (9 May 2016).
"Black Holes Produce Complexity Fastest" . Physics . 9 : 49.
Bibcode :
2016PhyOJ...9...49H .
doi :
10.1103/Physics.9.49 .
^ Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard; Swingle, Brian; Zhao, Ying (2016-05-09). "Complexity Equals Action". Physical Review Letters . 116 (19): 191301.
arXiv :
1509.07876 .
doi :
10.1103/PhysRevLett.116.191301 .
ISSN
0031-9007 .
PMID
27232013 .
^
a
b Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard; Swingle, Brian; Zhao, Ying (2016-04-18). "Complexity, action, and black holes". Physical Review D . 93 (8): 086006.
arXiv :
1512.04993 .
Bibcode :
2016PhRvD..93h6006B .
doi :
10.1103/PhysRevD.93.086006 .
ISSN
2470-0010 .
S2CID
55031668 .
^ Carmi, Dean; Myers, Robert C.; Rath, Pratik (March 2017). "Comments on Holographic Complexity". Journal of High Energy Physics . 2017 (3): 118.
arXiv :
1612.00433 .
Bibcode :
2017JHEP...03..118C .
doi :
10.1007/JHEP03(2017)118 .
ISSN
1029-8479 .
S2CID
111385742 .
^ Haferkamp, Jonas; Faist, Philippe; Kothakonda, Naga B. T.; Eisert, Jens; Yunger Halpern, Nicole (2022-03-28).
"Linear growth of quantum circuit complexity" . Nature Physics . 18 (5): 528–532.
arXiv :
2106.05305 .
Bibcode :
2022NatPh..18..528H .
doi :
10.1038/s41567-022-01539-6 .
ISSN
1745-2481 .
S2CID
235390872 .