From Ramanujan Graphs to Ramanujan Complexes [article]

Alexander Lubotzky, Ori Parzanchevski
2019 arXiv   pre-print
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.
arXiv:1904.03533v1 fatcat:2xohc75slbckddgjawpa5jg3iu