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

TL;DR

This paper introduces new quantum Floquet codes derived from hyperbolic semi-regular tessellations on various surfaces, expanding previous constructions and analyzing their performance and asymptotic properties.

Contribution

It generalizes hyperbolic Floquet code constructions to non-orientable surfaces and provides a detailed performance and asymptotic analysis.

Findings

Codes constructed on hyperbolic tessellations exhibit specific performance characteristics.

The asymptotic behavior of these codes is characterized and analyzed.

New constructions extend Floquet codes to 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 $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.