SYK code

SYK code[1,2]

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

SYK codes can have a constant rate and distance scaling as \(n^c\) for some power \(c\) [2].

Threshold

The coherent information of noise channels that either break or conserve fermion parity has been calculated for the SYK thermofield double state [7].

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 [8].

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”, Quantum 8, 1439 (2024) arXiv:2310.07770 DOI
[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]: J. Kim, E. Altman, and J. Y. Lee, “Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking”, (2024) arXiv:2410.24225
[8]: 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.