Holographic tensor network models and quantum error correction: a topical review

2021/02/04 by Alexander Jahn, A. Jahn, Jens Eisert · 1 voice
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum many-body systems #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1088/2058-9565/ac0293

arxiv published 2021/02/04 · openalex publication_date 2021/05/18 · arxiv updated 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Abstract Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks which not only give rise to physically meaningful correlations of holographic boundary states, but also reproduce and refine features of quantum error correction in holography. This topical review provides an overview over recent successful realizations of such models. It does so by building on an introduction of the theoretical foundations of AdS/CFT and necessary quantum information concepts, many of which have themselves developed into independent, rapidly evolving research fields.

Citations

• Entanglement Entropy at Large Central Charge
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• Geometric interpretation of the multi-scale entanglement renormalization ansatz
• Holographic Tensor Networks in Full AdS/CFT
• Magic entanglement renormalization for quantum fields
• Thermal states are vital: Entanglement Wedge Reconstruction from Operator-Pushing
• Fault-Tolerant Operation of a Quantum Error-Correction Code

Discussions

• Back in 2021, @jenseisert.bsky.social and I wrote a review on holographic tensor-network codes that just reached 100 citations! Glad to see this field being of interest to a growing crowd. Perhaps we' [bsky, 2 points, 0 comments]