Abstract
In this paper, we construct new families of asymmetric quantum surface codes (AQSCs) over non-orientable surfaces of genus g≥ 2 by applying tools of hyperbolic geometry. More precisely, we prove that if the genus g of a non-orientable surface is even (g=2h), then the parameters of the corresponding AQSC are equal to the parameters of a surface code obtained from an orientable surface of genus h. Additionally, if S is a non-orientable surface of genus g, we show that the new surface code constructed on a {p, q} tessellation over S has the ratio k/n better than the ratio of an AQSC constructed on the same {p, q} tessellation over an orientable surface of the same genus g.