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<p>In this paper, we describe the construction of new quantum surfaces and color codes on compact, non-orientable surfaces with genera of at least three. To obtain the codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on these surfaces. This method generalizes similar constructions of the hyperbolic surface codes and hyperbolic color codes on connected and compact surfaces, with genus <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, existing in the literature, and it can result in codes with excellent parameters. We also present tables containing several examples of these codes, some of which have never been shown before.</p>

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Surface and color codes from semi-regular tessellations on non-orientable surfaces

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Eduardo Brandani da Silva,
  • Douglas Fernando Copatti,
  • Waldir Silva Soares Jr.,
  • Evandro Mazetto Brizola

摘要

In this paper, we describe the construction of new quantum surfaces and color codes on compact, non-orientable surfaces with genera of at least three. To obtain the codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on these surfaces. This method generalizes similar constructions of the hyperbolic surface codes and hyperbolic color codes on connected and compact surfaces, with genus \(g \ge 2\) g ≥ 2 , existing in the literature, and it can result in codes with excellent parameters. We also present tables containing several examples of these codes, some of which have never been shown before.