New classes of TQC associated with self-dual, quasi self-dual and denser tessellations (pp0956-0970)
          C. D. Albuquerque, R. Palazzo Jr., and E. B. Silva
          doi: https://doi.org/10.26421/QIC10.11-12-6
Abstracts: In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus g ≥ 2. These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that k/n → 1 as n → ∞, except for the one case where k/n → 1/3 as n → ∞.
Key words: Topological quantum codes, Quantum error-correcting codes, Surface codes, Tessellations