Construction of quantum codes with large minimum distance from hyperbolic tessellations

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Authors

Avaz Naghipour¹

1. Department of Computer Engineering, University College of Nabi Akram

Conference / event

4th Asian Conference on Science, Technology & Medicine, November 2021 (Virtual)

Poster summary

In this paper we construct a large number of quantum codes on compact surfaces with genus derived from hyperbolic tessellations with large minimum distance and encoding rate asymptotically going to 1 while n tends to infinity. These quantum codes are associated with embeddings of complete bipartite graphs. We also show a table comparing the rate of these quantum codes when the minimum distance of code is at least four.

Keywords

Quantum codes, Compact surfaces, Hyperbolic tessellations, Embeddings, Complete bipartite graphs

Research areas

Computer and Information Science

References

1. Naghipour, A.: Construction of quantum codes from new embeddings of graphs on compact surfaces, Optical and Quantum Electronics, 2020, 40, pp. 1-13.
2. Soares Jr., W. S. and da Silva, E. B.: Hyperbolic quantum color codes, Quantum Information and Computation, 2018, 18, pp. 307-318.
3. de Albuquerque, C. D., Palazzo Jr., R. and da Silva, E. B.: Families of classes of topological quantum codes from tessellations {4i+2,2i+1}, {4i,4i}, {8i-4,4} and {12i-6,3}, Quantum Information and Computation, 2014, 14, pp. 1424-1440.

Funding

1. No data provided

Supplemental files

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Additional information

Competing interests

No competing interests were disclosed.

Data availability statement

Data sharing not applicable to this poster as no datasets were generated or analyzed during the current study.

Creative Commons license

Copyright © 2023 Naghipour. This is an open access work distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.