1. From Ramanujan graphs to Ramanujan complexes.
- Author
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Lubotzky, Alexander and Parzanchevski, Ori
- Subjects
QUANTUM computing ,RANDOM walks ,APPLICATION software ,COMPUTER science ,COMBINATORICS - Abstract
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high-dimensional theory has emerged. In this paper, these developments are surveyed. After explaining their connection to the Ramanujan conjecture, we will present some old and new results with an emphasis on random walks on these discrete objects and on the Euclidean spheres. The latter lead to 'golden gates' which are of importance in quantum computation. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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