\(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code[1]
Description
A non-CSS multimode GKP code defined on a 2D mode lattice that encodes a qudit logical space and whose excitations are characterized by the \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons theory. The code can be obtained from the analog surface code by condensing certain anyons [1].
The \(U(1)_{2} \times U(1)_{-4}\) case admits a topological order that is Witt non-trivial, i.e., that does not admit a gapped boundary. This order is not chiral (i.e., chiral central charge is zero) and does not admit a bosonic anyon.
Cousins
- Abelian topological code— The \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code realizes \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons theory on bosonic modes. The code can be obtained from the analog surface code by condensing certain anyons [1].
- Analog surface code— The \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code can be obtained from the analog surface code by condensing certain anyons [1].
Primary Hierarchy
Parents
\(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code
References
- [1]
- J. C. M. de la Fuente, T. D. Ellison, M. Cheng, and D. J. Williamson, “Topological stabilizer models on continuous variables”, (2025) arXiv:2411.04993
Page edit log
- Victor V. Albert (2024-12-04) — most recent
Cite as:
“\(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/chern_simons_gkp