3D Bacon-Shor code

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.

Transversal Gates

Logical CCZ gates on three codeblocks 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 (CSS-Plaquette) codes admit sheet-like (string-like) stabilizer generators.

Member of code lists

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 (2024-12-22) — most recent

Primary Hierarchy

Cite as:

“3D Bacon-Shor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_bacon_shor

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/topological/other/3d_bacon_shor.yml.