Built on

R. Landauer, “Irreversibility and heat generation in the computing processÕ”, IBM J. Res. Develop., 183Ð191 (1961)
1961
Earlier work this paper cites.
John Milnor, Curvatures of Left Invariant Metrics on Lie Groups, Advances in Mathematics 21, 293-329 (1976)
1976
Earlier work this paper cites.
Y. Aharonov and J. Anandan, “Phase Change During a Cyclic Quantum Evolution,” Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
W.H. Zurek, “Algorithmic randomness and physical entropy,” Phys. Rev. A 40
1989
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
C. H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W.H. Zurek, “Thermodynamics of computation and information distance,” Proceedings of STOC ’93, 21-30 (1993)
1993
Earlier work this paper cites.
S. Lloyd, “Computational Capacity of the Universe”, Physical Review Letters 88
2002
Earlier work this paper cites.
L. Susskind and J. Lindesay, “An introduction to black holes, information and the string theory revolution: The holographic universe,” Hackensack, USA: World Scientific (2005) 183 p
2005
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Earlier work this paper cites.

Similar

E. Knill and R. Laflamme, “On the power of one bit of quantum information,” Phys. Rev. Lett. 81
Original
2008
Cited alongside, same era.
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 1302
Original
2013
Cited alongside, same era.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, “Towards the Fast Scrambling Conjecture,” JHEP 1304
Original
2013
Cited alongside, same era.
D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90
Original
2014
Cited alongside, same era.
S. H. Shenker and D. Stanford, “Multiple Shocks,” JHEP 1412
Original

Then

L. Susskind, “The Typical-State Paradox: Diagnosing Horizons with Complexity,” Fortsch. Phys. 64
Original
2016
Later among the works it cites.
J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos,” JHEP 1608
Original
2016
Later among the works it cites.
J. Polchinski and V. Rosenhaus, “The Spectrum in the Sachdev-Ye-Kitaev Model,” JHEP 1604
Original
2016
Later among the works it cites.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116
Original

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2017

The Second Law of Quantum Complexity

Brown, Adam R., Susskind, Leonard

Understand

We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity".

To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$ qubits, and the positional entropy of a related classical system with $2^K$ degrees of freedom.
We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian.
We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system.

Built on

R. Landauer, “Irreversibility and heat generation in the computing processÕ”, IBM J. Res. Develop., 183Ð191 (1961)
1961
Earlier work this paper cites.
John Milnor, Curvatures of Left Invariant Metrics on Lie Groups, Advances in Mathematics 21, 293-329 (1976)
1976
Earlier work this paper cites.
Y. Aharonov and J. Anandan, “Phase Change During a Cyclic Quantum Evolution,” Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
W.H. Zurek, “Algorithmic randomness and physical entropy,” Phys. Rev. A 40
1989
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
C. H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W.H. Zurek, “Thermodynamics of computation and information distance,” Proceedings of STOC ’93, 21-30 (1993)
1993
Earlier work this paper cites.
S. Lloyd, “Computational Capacity of the Universe”, Physical Review Letters 88
2002
Earlier work this paper cites.
L. Susskind and J. Lindesay, “An introduction to black holes, information and the string theory revolution: The holographic universe,” Hackensack, USA: World Scientific (2005) 183 p
2005
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Earlier work this paper cites.

Similar

E. Knill and R. Laflamme, “On the power of one bit of quantum information,” Phys. Rev. Lett. 81
Original
2008
Cited alongside, same era.
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 1302
Original
2013
Cited alongside, same era.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, “Towards the Fast Scrambling Conjecture,” JHEP 1304
Original
2013
Cited alongside, same era.
D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90
Original
2014
Cited alongside, same era.
S. H. Shenker and D. Stanford, “Multiple Shocks,” JHEP 1412
Original

Then

L. Susskind, “The Typical-State Paradox: Diagnosing Horizons with Complexity,” Fortsch. Phys. 64
Original
2016
Later among the works it cites.
J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos,” JHEP 1608
Original
2016
Later among the works it cites.
J. Polchinski and V. Rosenhaus, “The Spectrum in the Sachdev-Ye-Kitaev Model,” JHEP 1604
Original
2016
Later among the works it cites.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2014

Cited alongside, same era.

G. Gour, M. P. Müller, V. Narasimhachar, R. W. Spekkens, N. Yunger Halpern, “The resource theory of informational nonequilibrium in thermodynamics”, arXiv:1309.6586; F. G. S. L. Brandao, M. Horodecki, J. Oppenheim, J. M. Renes, R. W. Spekkens, “The Resource Theory of Quantum States Out of Thermal Equilibrium”, Phys. Rev. Lett. 111

Original

2014

Cited alongside, same era.

A. Kitaev. A simple model of quantum holography - 2015. KITP strings seminar and Entanglement program (Feb. 12, April 7, and May 27, 2015). http://online.kitp.ucsb.edu/online/entangled15/

2015

Cited alongside, same era.

L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64

Original

2016

Cited alongside, same era.

L. Susskind and Y. Zhao, “Switchbacks and the Bridge to Nowhere,” arXiv:1408.2823 [hep-th]

Original

Cited in the paper.

A. R. Brown, L. Susskind and Y. Zhao, “Quantum Complexity and Negative Curvature,” arXiv:1608.02612 [hep-th]

Original

Cited in the paper.