Tessellation and constellations in the hyperbolic plane and applications to topological quantum coding

• Grant number: 14/25463-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: March 01, 2015
• End date: January 31, 2016
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Marcelo Firer
• Grantee: Marcelo Firer
• Visiting researcher: Eduardo Brandani da Silva
• Visiting researcher institution: Universidade Estadual de Maringá (UEM). Centro de Ciências Exatas (CCE), Brazil
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/25977-7 - Security and reliability of Information: theory and practice, AP.TEM

Abstract

This project addresses two specific instances in the coding universe, contexts in which the visiting researcher already has previous experience.The first of these is the use of tiling in the hyperbolic plane, or a choice of an hyperbolic lattice, for the development of high density signal constellations (making them suitable for quantization information), which are associated with the group structure, which allows development of algorithms for decoding.The second of these contexts refers to the use of (Euclidean an Hyperbolic) toric codes for quantum quantization, which is considered to be one of the promising development directions in quantum codification. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIRER, MARCELO; COUTO, KARINE BOBADILHA; DA SILVA, EDUARDO BRANDANI. Enumeration of Vertices, Edges and Polygons in Tessellations of the Plane. JOURNAL OF INTEGER SEQUENCES, v. 20, n. 10, 2017. (14/25463-6)