3D subsystem surface code[1]
Also known as 3D subsystem toric code.
Description
Subsystem generalization of the surface code on a 3D cubic lattice with gauge-group generators of weight at most three.
Parents
- Subsystem CSS code
- Lattice subsystem code
- Single-shot code — The 3D subsystem surface code is a single-shot code [1,2]; see Ref. [3] for an alternative formulation.
Cousins
- 3D surface code
- Self-correcting quantum code — The 3D subsystem surface code is not a self-correcting quantum memory despite being a single-shot code [4].
- Abelian quantum-double stabilizer code — The 3D subsystem surface code Hamiltonian phase diagram exhibits \(\mathbb{Z}_2\) topological order [4].
References
- [1]
- A. Kubica and M. Vasmer, “Single-shot quantum error correction with the three-dimensional subsystem toric code”, Nature Communications 13, (2022) arXiv:2106.02621 DOI
- [2]
- J. C. Bridgeman, A. Kubica, and M. Vasmer, “Lifting Topological Codes: Three-Dimensional Subsystem Codes from Two-Dimensional Anyon Models”, PRX Quantum 5, (2024) arXiv:2305.06365 DOI
- [3]
- C. Stahl, “Single-Shot Quantum Error Correction in Intertwined Toric Codes”, (2023) arXiv:2307.08118
- [4]
- Y. Li et al., “Phase diagram of the three-dimensional subsystem toric code”, (2023) arXiv:2305.06389
Page edit log
- Victor V. Albert (2023-05-12) — most recent
Cite as:
“3D subsystem surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/3d_subsystem_surface