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Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence

Pastawski, Fernando and Yoshida, Beni and Harlow, Daniel and Preskill, John (2015) Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence. Journal of High Energy Physics, 2015 (6). Art. No. 149. ISSN 1029-8479. doi:10.1007/JHEP06(2015)149.

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We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].

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Additional Information:© 2015 The Authors. Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: April 22, 2015; Accepted: May 26, 2015; Published: June 23, 2015. We thank Ning Bao, Oliver Buerschaper, Glen Evenbly, Daniel Gottesman, Aram Harrow, Isaac Kim, Seth Lloyd, Nima Lashkari, Hirosi Ooguri, Grant Salton, Kristan Temme, Guifre Vidal and Xiaoliang Qi for useful comments and discussions. We also have enjoyed discussions with Ahmed Almheiri, Xi Dong, and Brian Swingle, and with Matthew Headrick, about their independent and upcoming related work. FP, BY, and JP acknowledge funding provided by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants No. PHY-0803371 and PHY-1125565). BY is supported by the David and Ellen Lee Postdoctoral fellowship. DH is supported by the Princeton Center for Theoretical Science.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Ellen Lee Postdoctoral FellowshipUNSPECIFIED
Princeton Center for Theoretical ScienceUNSPECIFIED
Subject Keywords:AdS-CFT Correspondence, Lattice Integrable Models
Issue or Number:6
Record Number:CaltechAUTHORS:20150717-122900464
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58922
Deposited By: Tony Diaz
Deposited On:21 Jul 2015 21:36
Last Modified:10 Nov 2021 22:12

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