Abstract
If the cyclic sequence of faces for all the vertices in a map are of the same types, then the map is a semi-equivelar map. In particular, a semi-equivelar is equivelar if the faces are the same type. Topological quantum codes are being introduced as an alternative quantum code. The homological quantum code is a subclass of topological quantum code. We produce a technique to construct homological quantum codes associate with semi-equivelar maps. We also present homological quantum codes associate with maps on the surfaces with Euler characteristic \(-1\), \(-2\). Furthermore, we will present fifteen classes of homological quantum codes associate with covering maps of the class of maps on the surface with Euler characteristic \(-1\) and \(-2\).
Dr. Dipendu Maity is supported by NBHM, DAE (No. 02011/9/2021-NBHM(R.P.)/R&D-II/9101) and Dr. Ashish Kumar Upadhyay is supported by SERB-DST, India.
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Bhowmik, D., Maity, D., Upadhyay, A.K. (2022). A New Class of Quantum Codes Associate with a Class of Maps. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_20
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