Built on

K. Goto, H. Marrochio, R. C. Myers, L. Queimada and B. Yoshida, Holographic complexity equals which action? , Journal of High Energy Physics 2019
Original
1901
Earlier work this paper cites.
E. Witten, Light Rays, Singularities, and All That , 1901.03928
Original
1901
Earlier work this paper cites.
A. R. Brown and L. Susskind, The Complexity Geometry of a Single Qubit , 1903.12621
Original
1903
Earlier work this paper cites.
P. Nayak, J. Sonner and M. Vielma, Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach , 1903.00478
Original
1903
Earlier work this paper cites.
No. v. 18 in American Mathematical Society. American Mathematical Society, 1934
M. Morse, The Calculus of Variations in the Large · 1934
Earlier work this paper cites.
V. Arnold, Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits , Annales de l’Institut Fourier 16
1966
Earlier work this paper cites.
University of Illinois Press, Champaign, IL, USA, 1966
J. V. Neumann, Theory of Self-Reproducing Automata · 1966
Earlier work this paper cites.
J. Milnor, Curvatures of left invariant metrics on lie groups , Advances in Mathematics 21
1976
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization , Phys. Rev. E 50
1994
Earlier work this paper cites.
J. Maldacena, Eternal black holes in anti-de sitter , Journal of High Energy Physics 2003
2003
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M. A. Nielsen, C. M. Dawson, J. L. Dodd, A. Gilchrist, D. Mortimer, T. J. Osborne et al., Quantum dynamics as a physical resource , Phys. Rev. A 67
2003
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu and A. C. Doherty, Quantum computation as geometry , Science 311
2006
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D. W. Berry, G. Ahokas, R. Cleve and B. C. Sanders, Efficient quantum algorithms for simulating sparse hamiltonians , Communications in Mathematical Physics 270
2007
Earlier work this paper cites.
T. Tao, The euler-arnold equation , https://terrytao.wordpress.com/2010/06/07/the-euler-arnold-equation/ (2010)
2010
Earlier work this paper cites.
A. M. Childs and R. Kothari, Simulating sparse hamiltonians with star decompositions , in Theory of Quantum Computation, Communication, and Cryptography (W. van Dam, V. M. Kendon and S. Severini, eds.), (Berlin, Heidelberg), pp. 94–103, Springer Berlin Heidelberg, 2011
2011
Earlier work this paper cites.
A. M. Childs and N. Wiebe, Hamiltonian simulation using linear combinations of unitary operations , Quantum Info. Comput. 12
2012
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.
A. Kitaev, A simple model of quantum holography , http://online.kitp.ucsb.edu/online/entangled15/kitaev/ (2015)
2015
Earlier work this paper cites.
P.-L. Giscard, K. Lui, S. J. Thwaite and D. Jaksch, An exact formulation of the time-ordered exponential using path-sums , Journal of Mathematical Physics 56
Original
2015
Earlier work this paper cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Holographic complexity equals bulk action? , Physical Review Letters 116
Original
2016
Earlier work this paper cites.

Similar

J. Maldacena and D. Stanford, Remarks on the sachdev-ye-kitaev model , Physical Review D 94
Original
2016
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Original
2016
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L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics , Adv. Phys. 65
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Cited alongside, same era.
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Then

R.-Q. Yang, C. Niu, C.-Y. Zhang and K.-Y. Kim, Comparison of holographic and field theoretic complexities for time dependent thermofield double states , JHEP 02
Original
2018
Later among the works it cites.
M. Moosa, Evolution of Complexity Following a Global Quench , JHEP 03
Original
2018
Later among the works it cites.
J. Molina-Vilaplana and A. Del Campo, Complexity Functionals and Complexity Growth Limits in Continuous MERA Circuits , JHEP 08
Original
2018
Later among the works it cites.
D. W. F. Alves and G. Camilo, Evolution of complexity following a quantum quench in free field theory , JHEP 06
Original
2018
Later among the works it cites.
J. M. Magán, Black holes, complexity and quantum chaos , JHEP 09

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2019

Quantum Complexity of Time Evolution with Chaotic Hamiltonians

Balasubramanian, Vijay, DeCross, Matthew, Kar, Arjun et al.

Understand

We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example.

This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space.
Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator $e^{-iHt}$ whose length grows linearly with time.
This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally.

Built on

K. Goto, H. Marrochio, R. C. Myers, L. Queimada and B. Yoshida, Holographic complexity equals which action? , Journal of High Energy Physics 2019
Original
1901
Earlier work this paper cites.
E. Witten, Light Rays, Singularities, and All That , 1901.03928
Original
1901
Earlier work this paper cites.
A. R. Brown and L. Susskind, The Complexity Geometry of a Single Qubit , 1903.12621
Original
1903
Earlier work this paper cites.
P. Nayak, J. Sonner and M. Vielma, Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach , 1903.00478
Original
1903
Earlier work this paper cites.
No. v. 18 in American Mathematical Society. American Mathematical Society, 1934
M. Morse, The Calculus of Variations in the Large · 1934
Earlier work this paper cites.
V. Arnold, Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits , Annales de l’Institut Fourier 16
1966
Earlier work this paper cites.
University of Illinois Press, Champaign, IL, USA, 1966
J. V. Neumann, Theory of Self-Reproducing Automata · 1966
Earlier work this paper cites.
J. Milnor, Curvatures of left invariant metrics on lie groups , Advances in Mathematics 21
1976
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization , Phys. Rev. E 50
1994
Earlier work this paper cites.
J. Maldacena, Eternal black holes in anti-de sitter , Journal of High Energy Physics 2003
2003
Earlier work this paper cites.
M. A. Nielsen, C. M. Dawson, J. L. Dodd, A. Gilchrist, D. Mortimer, T. J. Osborne et al., Quantum dynamics as a physical resource , Phys. Rev. A 67
2003
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu and A. C. Doherty, Quantum computation as geometry , Science 311
2006
Earlier work this paper cites.
D. W. Berry, G. Ahokas, R. Cleve and B. C. Sanders, Efficient quantum algorithms for simulating sparse hamiltonians , Communications in Mathematical Physics 270
2007
Earlier work this paper cites.
T. Tao, The euler-arnold equation , https://terrytao.wordpress.com/2010/06/07/the-euler-arnold-equation/ (2010)
2010
Earlier work this paper cites.
A. M. Childs and R. Kothari, Simulating sparse hamiltonians with star decompositions , in Theory of Quantum Computation, Communication, and Cryptography (W. van Dam, V. M. Kendon and S. Severini, eds.), (Berlin, Heidelberg), pp. 94–103, Springer Berlin Heidelberg, 2011
2011
Earlier work this paper cites.
A. M. Childs and N. Wiebe, Hamiltonian simulation using linear combinations of unitary operations , Quantum Info. Comput. 12
2012
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.
A. Kitaev, A simple model of quantum holography , http://online.kitp.ucsb.edu/online/entangled15/kitaev/ (2015)
2015
Earlier work this paper cites.
P.-L. Giscard, K. Lui, S. J. Thwaite and D. Jaksch, An exact formulation of the time-ordered exponential using path-sums , Journal of Mathematical Physics 56
Original
2015
Earlier work this paper cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Holographic complexity equals bulk action? , Physical Review Letters 116
Original
2016
Earlier work this paper cites.

Similar

J. Maldacena and D. Stanford, Remarks on the sachdev-ye-kitaev model , Physical Review D 94
Original
2016
Cited alongside, same era.
J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model , JHEP 04
Original
2016
Cited alongside, same era.
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics , Adv. Phys. 65
Original
2016
Cited alongside, same era.
A. R. Brown, L. Susskind and Y. Zhao, Quantum complexity and negative curvature , Phys. Rev. D 95
Original
2017
Cited alongside, same era.
J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker et al., Black holes and random matrices , Journal of High Energy Physics 2017

Then

R.-Q. Yang, C. Niu, C.-Y. Zhang and K.-Y. Kim, Comparison of holographic and field theoretic complexities for time dependent thermofield double states , JHEP 02
Original
2018
Later among the works it cites.
M. Moosa, Evolution of Complexity Following a Global Quench , JHEP 03
Original
2018
Later among the works it cites.
J. Molina-Vilaplana and A. Del Campo, Complexity Functionals and Complexity Growth Limits in Continuous MERA Circuits , JHEP 08
Original
2018
Later among the works it cites.
D. W. F. Alves and G. Camilo, Evolution of complexity following a quantum quench in free field theory , JHEP 06
Original
2018
Later among the works it cites.
J. M. Magán, Black holes, complexity and quantum chaos , JHEP 09

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2017

Cited alongside, same era.

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