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].
SYK codes can have a constant rate and distance scaling as \(n^c\) for some power \(c\) .
- Fermionic 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 .
- 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 , the large distance of these codes can be interpreted as being due to the emergence of a wormhole.
- V. Chandrasekaran and A. Levine, “Quantum error correction in SYK and bulk emergence”, Journal of High Energy Physics 2022, (2022) arXiv:2203.05058 DOI
- G. Bentsen, P. Nguyen, and B. Swingle, “Approximate Quantum Codes From Long Wormholes”, (2023) arXiv:2310.07770
- 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
- Kitaev, Alexei. "A simple model of quantum holography (part 2)." Entanglement in Strongly-Correlated Quantum Matter (2015): 38.
- J. Kim, X. Cao, and E. Altman, “Low-rank Sachdev-Ye-Kitaev models”, Physical Review B 101, (2020) arXiv:1910.10173 DOI
- J. Kim, E. Altman, and X. Cao, “Dirac fast scramblers”, Physical Review B 103, (2021) arXiv:2010.10545 DOI
Page edit log
- Victor V. Albert (2023-10-16) — most recent
“SYK code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/syk