3D subsystem surface code

3D subsystem surface code[1]

Alternative names: 3D subsystem toric code.

Subsystem generalization of the surface code on a 3D cubic lattice with gauge-group generators of weight at most three.

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 [2].
Abelian quantum-double stabilizer code— The 3D subsystem surface code Hamiltonian phase diagram exhibits \(\mathbb{Z}_2\) topological order [2].

Parents

The 3D subsystem surface code is a single-shot code [1,3]; see Ref. [4] for an alternative formulation.

3D subsystem surface code

[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]: Y. Li, C. W. von Keyserlingk, G. Zhu, and T. Jochym-O’Connor, “Phase diagram of the three-dimensional subsystem toric code”, Physical Review Research 6, (2024) arXiv:2305.06389 DOI
[3]: 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
[4]: C. Stahl, “Single-shot quantum error correction in intertwined toric codes”, Physical Review B 110, (2024) arXiv:2307.08118 DOI

Page edit log

“3D subsystem surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/3d_subsystem_surface