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2023

Holographic Codes from Hyperinvariant Tensor Networks

Steinberg, Matthew, Feld, Sebastian, Jahn, Alexander

Understand

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom.

Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery.
However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states.
In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions.

Built on

C. Akers, S. Leichenauer, and A. Levine, Phys. Rev. D 100
Original
1908
Earlier work this paper cites.
J. M. Maldacena, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
E. Witten, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
A. Jahn, Z. Zimborás, and J. Eisert, Quantum 6
Original
2004
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
T. Faulkner, (2020), arXiv:2008.04810 [hep-th]
Original
2008
Earlier work this paper cites.
G. Vidal, Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
R. N. C. Pfeifer, G. Evenbly, and G. Vidal, Phys. Rev. A 79
Original
2009
Earlier work this paper cites.
C. Cao and B. Lackey, JHEP 05
Original
2010
Earlier work this paper cites.
T. Faulkner, A. Lewkowycz, and J. Maldacena, JHEP 11
Original
2013
Earlier work this paper cites.
A. Lewkowycz and J. Maldacena, JHEP 08
Original
2013
Earlier work this paper cites.
T. Barrella, X. Dong, S. A. Hartnoll, and V. L. Martin, JHEP 09
Original
2013
Earlier work this paper cites.
A. Almheiri, X. Dong, and D. Harlow, JHEP 04
Original
2015
Earlier work this paper cites.
N. Engelhardt and A. C. Wall, JHEP 01
Original
2015
Earlier work this paper cites.
F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill, JHEP 06
Original
2015
Earlier work this paper cites.

Similar

D. Goyeneche, D. Alsina, J. I. Latorre, A. Riera, and K. Życzkowski, Physical Review A 92
2015
Cited alongside, same era.
X. Dong, D. Harlow, and A. C. Wall, Phys. Rev. Lett. 117
Original
2016
Cited alongside, same era.
N. Bao and I. H. Kim, (2016), arXiv:1601.07616 [hep-th]
Original
2016
Cited alongside, same era.
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, JHEP 11
Original
2016
Cited alongside, same era.
M. Enriquez, I. Wintrowicz, and K. Życzkowski, in Journal of Physics Conference Series , Journal of Physics Conference Series, Vol. 698 (2016) p. 012003
2016
Cited alongside, same era.

Then

P. Hayden and G. Penington, JHEP 12
Original
2019
Later among the works it cites.
Y. Ling, Y. Liu, Z.-Y. Xian, and Y. Xiao, Phys. Rev. D 99
Original
2019
Later among the works it cites.
Z. Raissi, IEEE Access 8
2020
Later among the works it cites.
Z. Raissi, A. Teixido, C. Gogolin, and A. Acin, Physical Review Research 2
2020
Later among the works it cites.
P. Mazurek, M. Farkas, A. Grudka, M. Horodecki, and M. Studziński, Physical Review A 101
2020
Later among the works it cites.
M. Doroudiani and V. Karimipour, Physical Review A 102
2020
Later among the works it cites.