Holographic code[1]
Description
Block quantum code whose features serve to model aspects of the AdS/CFT holographic duality and, more generally, quantum gravity.Cousins
- Approximate quantum error-correcting code (AQECC)— Universal subspace approximate error correction is used to model black holes [4].
- Approximate operator-algebra QECC— Properties of holographic codes are often quantified in the Heisenberg picture, i.e., in terms of operator algebras [5–8].
- 2D lattice stabilizer code— 2D lattice stabilizer codes admit a bulk-boundary correspondence similar to that of holographic codes, namely, the boundary Hilbert space of the former cannot be realized via local degrees of freedom [9].
- Gottesman-Kitaev-Preskill (GKP) code— GKP codespaces exist in the CFT dual of a particular holographic framework [10,11].
Member of code lists
Primary Hierarchy
Parents
Holographic code
Children
Matrix-model codes are motivated by the Ads/CFT correspondence because it is manifest in continuous non-Abelian gauge theories with large gauge groups [12].
The RG cat code encoder has coarse-graining features reminiscent of holography [7].
Holographic codes whose encoders are holographic tensor networks are holographic tensor-network codes.
CFT codewords lie in the low-energy subspace of a conformal field theory (CFT), e.g., the quantum Ising model at its critical point.
The robustness of KPT codes does not rely on arguments from holographic duality, but such codes do aim to describe interiors of black holes.
References
- [1]
- F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill, “Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence”, Journal of High Energy Physics 2015, (2015) arXiv:1503.06237 DOI
- [2]
- A. Jahn and J. Eisert, “Holographic tensor network models and quantum error correction: a topical review”, Quantum Science and Technology 6, 033002 (2021) arXiv:2102.02619 DOI
- [3]
- T. Kibe, P. Mandayam, and A. Mukhopadhyay, “Holographic spacetime, black holes and quantum error correcting codes: a review”, The European Physical Journal C 82, (2022) arXiv:2110.14669 DOI
- [4]
- P. Hayden and G. Penington, “Learning the Alpha-bits of black holes”, Journal of High Energy Physics 2019, (2019) arXiv:1807.06041 DOI
- [5]
- A. Almheiri, X. Dong, and D. Harlow, “Bulk locality and quantum error correction in AdS/CFT”, Journal of High Energy Physics 2015, (2015) arXiv:1411.7041 DOI
- [6]
- F. Pastawski and J. Preskill, “Code Properties from Holographic Geometries”, Physical Review X 7, (2017) arXiv:1612.00017 DOI
- [7]
- K. Furuya, N. Lashkari, and S. Ouseph, “Real-space RG, error correction and Petz map”, Journal of High Energy Physics 2022, (2022) arXiv:2012.14001 DOI
- [8]
- N. Bao and J. Naskar, “Code properties of the holographic Sierpinski triangle”, Physical Review D 106, (2022) arXiv:2203.01379 DOI
- [9]
- T. Schuster, N. Tantivasadakarn, A. Vishwanath, and N. Y. Yao, “A holographic view of topological stabilizer codes”, (2023) arXiv:2312.04617
- [10]
- A. Guevara and Y. Hu, “Celestial Quantum Error Correction I: Qubits from Noncommutative Klein Space”, (2023) arXiv:2312.16298
- [11]
- A. Guevara and Y. Hu, “Celestial Quantum Error Correction II: From Qudits to Celestial CFT”, (2025) arXiv:2412.19653
- [12]
- C. Cao, G. Cheng, and B. Swingle, “Large \(N\) Matrix Quantum Mechanics as a Quantum Memory”, (2022) arXiv:2211.08448
- [13]
- G. Bentsen, P. Nguyen, and B. Swingle, “Approximate Quantum Codes From Long Wormholes”, Quantum 8, 1439 (2024) arXiv:2310.07770 DOI
Page edit log
- Victor V. Albert (2022-03-08) — most recent
- Joel Rajakumar (2021-12-20)
Cite as:
“Holographic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/holographic