Built on

J. M. Maldacena, “The Large N N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
M. Bañados, “Three-dimensional quantum geometry and black holes,” AIP Conf. Proc. 484
1999
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, “Entanglement renormalization,” Phys. Rev. Lett. 99
2008
Earlier work this paper cites.
B. Swingle, “Entanglement renormalization and holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D 48
2013
Earlier work this paper cites.

Similar

J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “Entanglement renormalization for quantum fields in real space,” Phys. Rev. Lett. 110
Original
2013
Cited alongside, same era.
C. Beny, “Causal structure of the entanglement renormalization ansatz,” New J. Phys. 15
Original
2013
Cited alongside, same era.
V. Balasubramanian, B. D. Chowdhury, B. Czech, J. de Boer and M. P. Heller, “Bulk curves from boundary data in holography,” Phys. Rev. D 89
Original
2014
Cited alongside, same era.
G. Evenbly and G. Vidal, “Tensor network renormalization,” Phys. Rev. Lett. 115
Original
2015
Cited alongside, same era.
G. Evenbly and G. Vidal, “Tensor network renormalization yields the multi-scale entanglement renormalization ansatz,” Phys. Rev. Lett. 115

Then

B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral geometry and holography,” JHEP 1510
Original
2016
Later among the works it cites.
J. de Boer, F. M. Haehl, M. P. Heller and R. C. Myers, “Entanglement, holography and causal diamonds,” JHEP 1608
Original
2016
Later among the works it cites.
G. Evenbly and G. Vidal, “Local scale transformations on the lattice with tensor network renormalization,” Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Tensor networks from kinematic space,” JHEP 1607
Original
2016
Later among the works it cites.
M. Miyaji, T. Takayanagi and K. Watanabe, “From path integrals to tensor networks for the AdS/CFT correspondence,” Phys. Rev. D 95

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2017

Einstein's Equations from Varying Complexity

Czech, Bartlomiej

Understand

A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime.

Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity.
I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space.
The argument relies on known facts about holography and on properties of Tensor Network Renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.

Built on

J. M. Maldacena, “The Large N N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
M. Bañados, “Three-dimensional quantum geometry and black holes,” AIP Conf. Proc. 484
1999
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, “Entanglement renormalization,” Phys. Rev. Lett. 99
2008
Earlier work this paper cites.
B. Swingle, “Entanglement renormalization and holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D 48
2013
Earlier work this paper cites.

Similar

J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “Entanglement renormalization for quantum fields in real space,” Phys. Rev. Lett. 110
Original
2013
Cited alongside, same era.
C. Beny, “Causal structure of the entanglement renormalization ansatz,” New J. Phys. 15
Original
2013
Cited alongside, same era.
V. Balasubramanian, B. D. Chowdhury, B. Czech, J. de Boer and M. P. Heller, “Bulk curves from boundary data in holography,” Phys. Rev. D 89
Original
2014
Cited alongside, same era.
G. Evenbly and G. Vidal, “Tensor network renormalization,” Phys. Rev. Lett. 115
Original
2015
Cited alongside, same era.
G. Evenbly and G. Vidal, “Tensor network renormalization yields the multi-scale entanglement renormalization ansatz,” Phys. Rev. Lett. 115

Then

B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral geometry and holography,” JHEP 1510
Original
2016
Later among the works it cites.
J. de Boer, F. M. Haehl, M. P. Heller and R. C. Myers, “Entanglement, holography and causal diamonds,” JHEP 1608
Original
2016
Later among the works it cites.
G. Evenbly and G. Vidal, “Local scale transformations on the lattice with tensor network renormalization,” Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Tensor networks from kinematic space,” JHEP 1607
Original
2016
Later among the works it cites.
M. Miyaji, T. Takayanagi and K. Watanabe, “From path integrals to tensor networks for the AdS/CFT correspondence,” Phys. Rev. D 95

Beyond the bibliography

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

Open on alphaXiv

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Original

2015

Cited alongside, same era.

A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic complexity equals bulk action?,” Phys. Rev. Lett. 116

Original

2016

Cited alongside, same era.

P. H. Ginsparg and G. W. Moore, “Lectures on 2-D gravity and 2-D string theory,” Yale Univ. New Haven - YCTP-P23-92 (92,rec.Apr.93) 197 p. Los Alamos Nat. Lab. - LA-UR-92-3479 (92,rec.Apr.93) 197 p. e: LANL hep-th/9304011 [hep-th/9304011]

Cited in the paper.

P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, “AdS from optimization of path integrals in CFTs,” arXiv:1703.00456 [hep-th]

Original

Cited in the paper.

Original

2017

Closest in time.