Surface codes and color codes associated with non-orientable surfaces

Abstract

Silva et al. produced quantum codes related to topology and coloring, which are associated with tessellations on the orientable surfaces of genus $\ge 1$ and the non-orientable surfaces of the genus 1. Current work presents an approach to build quantum surface and color codes} on non-orientable surfaces of genus $ \geq 2n+1 $ for $n\geq 1$. We also present several tables of new surface and color codes related to non-orientable surfaces. These codes have the ratios $k/n$ and $d/n$ better than the codes obtained from orientable surfaces.