## Description

Approximate \(n\)-fermionic code whose codewords are low-energy states of the Sachdev-Ye-Kitaev (SYK) Hamiltonian [3,4] or other low-rank SYK models [5,6].

## Rate

## Parents

- Fermion code
- Approximate quantum error-correcting code (AQECC) — SYK codes are approximately error correcting in that they satisfy certain error-correction conditions based on mutual information [2].
- Hamiltonian-based code — The SYK code Hamiltonian is constructed out of non-commuting few-site terms, and every fermion participates in many interactions.
- Holographic code — In a holographic model [2], the large distance of these codes can be interpreted as being due to the emergence of a wormhole.

## Cousin

- Kim-Preskill-Tang (KPT) code — The Brownian SYK model can be used to demonstrate the complexity-based error-correction of KPT codes [7].

## References

- [1]
- V. Chandrasekaran and A. Levine, “Quantum error correction in SYK and bulk emergence”, Journal of High Energy Physics 2022, (2022) arXiv:2203.05058 DOI
- [2]
- G. Bentsen, P. Nguyen, and B. Swingle, “Approximate Quantum Codes From Long Wormholes”, (2024) arXiv:2310.07770
- [3]
- S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet”, Physical Review Letters 70, 3339 (1993) arXiv:cond-mat/9212030 DOI
- [4]
- Kitaev, Alexei. "A simple model of quantum holography (part 2)." Entanglement in Strongly-Correlated Quantum Matter (2015): 38.
- [5]
- J. Kim, X. Cao, and E. Altman, “Low-rank Sachdev-Ye-Kitaev models”, Physical Review B 101, (2020) arXiv:1910.10173 DOI
- [6]
- J. Kim, E. Altman, and X. Cao, “Dirac fast scramblers”, Physical Review B 103, (2021) arXiv:2010.10545 DOI
- [7]
- I. Kim, E. Tang, and J. Preskill, “The ghost in the radiation: robust encodings of the black hole interior”, Journal of High Energy Physics 2020, (2020) arXiv:2003.05451 DOI

## Page edit log

- Victor V. Albert (2023-10-16) — most recent

## Cite as:

“SYK code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/syk

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/holographic/syk.yml.