Description
Lattice stabilizer code in three Euclidean dimensions.
For translation-invariant qubit topological stabilizer models in 3D, bulk commutation data can be used to coarsely sort phases into topological quantum field theory (TQFT), foliated type-I, fractal type-I, and type-II sectors [1]. For the TQFT sector, the paper conjectures equivalence under a locality-preserving unitary to copies of the 3D surface code and/or the 3D fermionic surface code, together with trivial ancillas [1].
Code Capacity Threshold
Applying Clifford deformations to various 3D stabilizer codes, including the 3D surface code, 3D color code, X-cube model code, and Sierpinski prism model code, yields a \(50\%\) code capacity threshold under infinitely biased Pauli noise [2].Cousins
- Clifford-deformed surface code (CDSC)— Applying Clifford deformation to various 3D stabilizer codes, including the 3D surface code, 3D color code, X-cube model code, the Sierpinski prism model code, yields a \(50\%\) code capacity threshold under infinitely biased Pauli noise [2].
- Asymmetric quantum code (AQC)— Applying Clifford deformation to various 3D stabilizer codes, including the 3D surface code, 3D color code, X-cube model code, the Sierpinski prism model code, yields a \(50\%\) code capacity threshold under infinitely biased Pauli noise [2].
- Abelian topological code— Translation-invariant qubit 3D TQFT stabilizer models are conjectured to be equivalent, under a locality-preserving unitary, to multiple copies of the 3D surface code and/or the 3D fermionic surface code together with trivial ancillas [1].
- Self-correcting quantum code— 3D translationally-invariant qubit stabilizer code families with constant \(k\) support logical string operators and thus cannot be self-correcting [3]. For non-constant \(k\), such families can support at most a logarithmic energy barrier [4].
Primary Hierarchy
Parents
3D lattice stabilizer code
Children
The 3D bosonization code encodes fermionic modes into a 3D qubit stabilizer code.
References
- [1]
- A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
- [2]
- E. Huang, A. Pesah, C. T. Chubb, M. Vasmer, and A. Dua, “Tailoring Three-Dimensional Topological Codes for Biased Noise”, PRX Quantum 4, (2023) arXiv:2211.02116 DOI
- [3]
- B. Yoshida, “Feasibility of self-correcting quantum memory and thermal stability of topological order”, Annals of Physics 326, 2566 (2011) arXiv:1103.1885 DOI
- [4]
- J. Haah, “Local stabilizer codes in three dimensions without string logical operators”, Physical Review A 83, (2011) arXiv:1101.1962 DOI
Page edit log
- Victor V. Albert (2024-01-27) — most recent
Cite as:
“3D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_stabilizer