\([[8,2,3]]\) Hermitian code [1]
Description
A non-CSS Hermitian eight-qubit stabilizer code that is the only Hermitian code and that has the largest automorphism group among the 20 inequivalent \([[8,2,3]]\) codes [2]. The code has an exceptionally short fault-tolerant syndrome measurement sequence [1,2].
A stabilizer tableau for the code is [3] \begin{align}
Decoding
Short Shor-style syndrome extraction circuits can be used for syndrome-based decoding [1].Fault Tolerance
Short Shor-style syndrome extraction circuits can be used for syndrome-based decoding [1].Cousins
- Concatenated qubit code— Applying concatenated symplectic doubling to the \([[8,2,3]]\) Hermitian code yields a \([[32,4,6]]\) self-dual CSS code [3; Corr. 2].
- Self-dual CSS code— Applying concatenated symplectic doubling to the \([[8,2,3]]\) Hermitian code yields a \([[32,4,6]]\) self-dual CSS code [3; Corr. 2].
- \([[4,2,2]]\) Four-qubit code— Applying concatenated symplectic doubling to the \([[8,2,3]]\) Hermitian code yields a \([[32,4,6]]\) self-dual CSS code [3; Corr. 2].
Primary Hierarchy
References
- [1]
N. Delfosse and B. W. Reichardt, “Short Shor-style syndrome sequences”, (2020) arXiv:2008.05051
- [2]
A. Cross and D. Vandeth, “Small Binary Stabilizer Subsystem Codes”, (2025) arXiv:2501.17447
- [3]
B. W. Reichardt, D. Aasen, and R. Chao, “Fire and ice: Partially fault-tolerant quantum computing with selective state filtering”, (2026) arXiv:2605.15344
- [4]
Qiskit Community, “Qiskit QEC framework”, URL
Page edit log
- Victor V. Albert (2026-08-25) — most recent
- Victor V. Albert (2026-06-08)
- Victor V. Albert (2026-05-12)
Cite as:
“\([[8,2,3]]\) Hermitian code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stab_8_2_3, arXiv:2606.11484