3D Bacon-Shor code [1]
Description
Generalization of the Bacon-Shor code to three dimensions that was conjectured to be a self-correcting memory. It is defined on a cubic lattice and admits sheet-like stabilizer generators.Protection
On an \(L\times L\times L\) cubic lattice, the symmetric family has parameters \([[L^3,1,L]]\) [1].Transversal and Permutation-Based Gates
Logical \(CCZ\) gates on three code blocks of different orientations [2].Threshold
The 3D Bacon-Shor code has two entanglement transitions [3].Cousins
- \(\mathbb{Z}^n\) hypercubic lattice— 3D Bacon-Shor codes are defined on a hypercubic lattice.
- Self-correcting quantum code— 3D Bacon-Shor codes were conjectured to be self-correcting [1], but there remain issues to be resolved in order to validate this conjecture (see [4; Sec. IX.B]).
- CSS-Plaquette code— 3D Bacon-Shor and CSS-Plaquette codes admit sheet-like and string-like stabilizer generators, respectively.
Primary Hierarchy
References
- [1]
D. Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories”, Physical Review A 73, (2006) arXiv:quant-ph/0506023 DOI
- [2]
T. J. Yoder, “Universal fault-tolerant quantum computation with Bacon-Shor codes”, (2017) arXiv:1705.01686
- [3]
B. Placke and S. A. Parameswaran, “Slow measurement-only dynamics of entanglement in Pauli subsystem codes”, (2024) arXiv:2405.14927
- [4]
B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, and J. R. Wootton, “Quantum memories at finite temperature”, Reviews of Modern Physics 88, (2016) arXiv:1411.6643 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-12-22)
Cite as:
“3D Bacon-Shor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/3d_bacon_shor, arXiv:2606.11484