🤖 AI Summary
This work addresses the construction of high-performance quantum Floquet codes on compact orientable and non-orientable surfaces. The authors represent such surfaces via hyperbolic polygons and, for the first time, extend the framework of semi-regular hyperbolic tessellations to the non-orientable setting, enabling a systematic design of encoding structures suitable for high-genus and non-orientable topologies. By integrating tools from hyperbolic geometry, surface topology classification, semi-regular tiling theory, and quantum error-correcting code design, they generate several new families of Floquet codes. Performance analysis and asymptotic studies demonstrate their superior error-correction capabilities on higher-dimensional topological surfaces, significantly generalizing the existing construction framework for high-genus Floquet codes.
📝 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.