\(D\)-dimensional twisted toric code[1]
Description
Extenstion of the Kitaev toric code to higher-dimensional lattices with shifted (a.k.a twisted) boundary conditions. Such boundary conditions yields quibit geometries that are tori \(\mathbb{R}^D/\Lambda\), where \(\Lambda\) is an arbitrary \(D\)-dimensional lattice. Picking a hypercubic lattice yields the ordinary \(D\)-dimensional toric code. It is conjectured that appropriate twisted boundary conditions yield multi-dimensional toric code families with linear distance and logarithmic-weight stabilizer generators [1].
Parent
Child
- Toric code — The \(D\)-dimensional twisted toric code reduces to the toric code for \(D=2\) and a square lattice.
Cousin
- Quantum low-density parity-check (QLDPC) code — It is conjectured that appropriate twisted boundary conditions yield multi-dimensional toric code families with linear distance and logarithmic-weight stabilizer generators [1].
References
- [1]
- M. B. Hastings, “Quantum Codes from High-Dimensional Manifolds”, (2016) arXiv:1608.05089
Page edit log
- Victor V. Albert (2024-05-03) — most recent
Cite as:
“\(D\)-dimensional twisted toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/higher_dimensional_toric