Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces

Abstract

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 $g\ge 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.