Compactified \(\mathbb{R}\) gauge theory code[1]
Description
An integer-homology bosonic CSS code realizing 2D \(U(1)\) gauge theory on bosonic modes. The code can be obtained from the analog surface code by condensing certain anyons [1]. This results in a pinning of each mode to the space of periodic functions, which make up a physical rotor, and can be thought of as compactification of the 2D \(\mathbb{R}\) gauge theory phase realized by the analog surface code.
Parents
- Integer-homology bosonic CSS code — The compactified \(\mathbb{R}\) gauge theory code realizes \(U(1)\) gauge theory on bosonic modes.
- 2D lattice stabilizer code
Cousins
- Analog surface code — The compactified \(\mathbb{R}\) gauge theory code can be obtained from the analog surface code by condensing certain anyons [1]. This results in a pinning of each mode to the space of periodic functions, which make up a physical rotor, and can be thought of as compactification of the 2D \(\mathbb{R}\) gauge theory phase realized by the analog surface code.
- Abelian topological code — The compactified \(\mathbb{R}\) gauge theory code can be obtained from the analog surface code by condensing certain anyons [1]. This results in a pinning of each mode to the space of periodic functions, which make up a physical rotor, and can be thought of as compactification of the 2D \(\mathbb{R}\) gauge theory phase realized by the analog surface code.
- Modular-qudit surface code — The tiger surface code can be thought of as a realization of the \(q\to\infty\) \(U(1)\) rotor limit [2] of the qudit surface code as a bosonic stabilizer code.
- Tiger surface code — Both the compactified \(\mathbb{R}\) gauge theory and tiger surface code are constructed from a hypergraph product of two repetition codes over the integers.
References
- [1]
- J. C. M. de la Fuente, T. D. Ellison, M. Cheng, and D. J. Williamson, “Topological stabilizer models on continuous variables”, (2024) arXiv:2411.04993
- [2]
- V. V. Albert, S. Pascazio, and M. H. Devoret, “General phase spaces: from discrete variables to rotor and continuum limits”, Journal of Physics A: Mathematical and Theoretical 50, 504002 (2017) arXiv:1709.04460 DOI
Page edit log
- Victor V. Albert (2024-12-04) — most recent
Cite as:
“Compactified \(\mathbb{R}\) gauge theory code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/compactified_r