Code Properties from Holographic Geometries
Open accessAbstract
Deep theoretical links may exist between how space encodes information and error correcting codes being developed for quantum computers. A new analysis explores these connections further and offers insights into not just error-correction codes but also how we interpret ideas about spacetime.
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In the holographic setting, if the boundary state is such that A→A→A3 form a quantum Markov chain, then there exists a recovery map that recovers for the erasure of H_A2 without involving the subsystem H_Ā.
“The quantum Markov condition states that this is indeed possible if the boundary state is such that A → A → A 3 form a quantum Markov chain, which will saturate the inequality in Eq. ( 65).Then, there exists a recovery map R : B(H A ) → B(H A ) that recovers for the erasure of H A 2 , without involving the subsystem H Ā.”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [178]
Cites
A covariant holographic entanglement entropy proposal
Hubeny, V. E., Rangamani, M., & Takayanagi, T. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/07/062 · Cited by 1,822 · cited 2× · see citing works
“[17] Veronika E Hubeny, Mukund Rangamani, and Tadashi Takayanagi.”
BackgroundA Covariant Holographic Entanglement Entropy Proposal
Hubeny, V. E., Rangamani, M., & Takayanagi, T. (2007) · arXiv · doi:10.48550/arxiv.0705.0016 · Cited by 1,822
Cool horizons for entangled black holes
Maldacena, J., & Susskind, L. (2013) · Fortschritte der Physik · doi:10.1002/prop.201300020 · Cited by 1,304 · see citing works
A covariant entropy conjecture
Bousso, R. (1999) · Journal of High Energy Physics · doi:10.1088/1126-6708/1999/07/004 · Cited by 850 · see citing works
Bulk locality and quantum error correction in AdS/CFT
Almheiri, A., Dong, X., & Harlow, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep04(2015)163 · Cited by 802 · see citing works
Local Random Quantum Circuits are Approximate Polynomial-Designs
Brandão, F. G. S. L., Harrow, A. W., & Horodecki, M. (2016) · Communications in Mathematical Physics · doi:10.1007/s00220-016-2706-8 · Cited by 404 · see citing works
Quantum error correction of observables
Bény, C., Kempf, A., & Kribs, D. W. (2007) · Physical Review A · doi:10.1103/physreva.76.042303 · Cited by 67 · see citing works
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Holographic spacetime, black holes and quantum error correcting codes: a review
Kibe, T., Mandayam, P., & Mukhopadhyay, A. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10382-1 · Cited by 44 · see citing works
“In such a situation, the erasure is said to locally correctable [178].”
BackgroundHolographic codes from hyperinvariant tensor networks
Steinberg, M., Feld, S., & Jahn, A. (2023) · Nature Communications · doi:10.1038/s41467-023-42743-z · Cited by 20 · see citing works
- Authors
- Pastawski, F., & Preskill, J.
- Affiliations
- Freie Universität Berlin (DE)
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2017-05-15
- Volume
- 7
- Issue
- 2
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W2559988517
- Cited by
- 52
- References
- 7
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 1 · 2023: 5 · 2022: 7 · 2021: 8 · 2020: 12 · 2019: 7 · 2018: 5 · 2017: 3
- FWCI
- 3.78
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver
- Funders
- National Science Foundation (NSF PHY-1125915NSF PHY-1125915)
- Gordon and Betty Moore Foundation
- Simons Foundation
- H2020 European Research Council
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- holography, holographic geometry, quantum error-correcting codes, quantum information encoding, spacetime, AdS/CFT correspondence, quantum error correction
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