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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.21 No.13&14 November 2021 |
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Surface codes and color codes associated with non-orientable
surfaces (pp1135-1153)
Debashis
Bhowmik, Dipendu Maity, and
Eduardo
Brandani Da Silva
doi:
https://doi.org/10.26421/QIC21.13-14-4
Abstracts:
Silva et al. produced quantum codes
related to topology and coloring, which are associated with
tessellations on the
orientable surfaces of genus
$\ge 1$
and the non-orientable
surfaces of the genus 1.
Current work presents an approach to
build
quantum surface and color codes} on non-orientable
surfaces of genus $ \geq 2n+1 $
for $n\geq 1$.
We also present several tables of new surface and color codes related to
non-orientable
surfaces. These codes have the ratios
$k/n$
and $d/n$
better than the codes obtained from
orientable surfaces.
Key words:
Topological
Quantum Code, Surface Code, Quantum
Color Code, Hyperbolic
Geometry |
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