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.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.

quant-pharXiv:2603.29811Apr 1, 20260 citations

Asymmetric quantum codes on non-orientable surfaces

Waldir Silva Soares, Douglas Fernando Copatti, Giuliano G. La Guardia +1 more

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 all asymmetric quantum surface codes constructed over orientable surfaces with genus h can be reproduced, with exactly the same parameters, over a non-orientable surface with genus g = 2h. Additionally, if S is a non-orientable surface of genus g, we show that the new surface code constructed on a {p, q} tessellation of S has ratio k/n greater than the ratio of an AQSC constructed on the same {p, q} tessellation over an orientable surface of the same genus g.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 all asymmetric quantum surface codes constructed over orientable surfaces with genus h can be reproduced, with exactly the same parameters, over a non-orientable surface with genus g = 2h. Additionally, if S is a non-orientable surface of genus g, we show that the new surface code constructed on a {p, q} tessellation of S has ratio k/n greater than the ratio of an AQSC constructed on the same {p, q} tessellation over an orientable surface of the same genus g.

arXiv:2303.14803Journal of Mathematical PhysicsJun 1, 20250 citations

Construction of quantum codes from new embeddings of graphs on compact surfaces

Avaz Naghipour

Optical and Quantum ElectronicsDec 17, 20192 citations

g \geq 2

. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.