Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces
This addresses quantum error correction for topological quantum computing, but appears incremental as it generalizes existing hyperbolic Floquet code methods.
The paper constructs new quantum Floquet codes on compact orientable and non-orientable surfaces by identifying them with hyperbolic polygons and examining semi-regular tessellations, generalizing prior constructions for surfaces with genus ≥2. It includes performance analysis and asymptotic behavior investigation.
In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.