5 papers
Ramanujan Bigraphs
Shai Evra, Brooke Feigon, Kathrin Maurischat +1
In their seminal paper, Lubotzky, Phillips and Sarnak (LPS) defined the notion of regular Ramanujan graphs and gave an explicit construction of infinite families of -regular…
Multi-Qubit Golden Gates
Rahul Dalal, Shai Evra, Ori Parzanchevski
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and su…
The Cohomological Sarnak-Xue Density Hypothesis for
Shai Evra, Mathilde Gerbelli-Gauthier, Henrik P. A. Gustafsson
We prove the cohomological version of the Sarnak--Xue Density Hypothesis for over a totally real field and for inner forms split at all finite places. The proof relies on…
Polynomial Bogolyubov for special linear groups via tensor rank
Shai Evra, Guy Kindler, Noam Lifshitz
We prove a polynomial Bogolyubov type lemma for the special linear group over finite fields. Specifically, we show that there exists an absolute constant such that if is…
Arithmeticity, thinness and efficiency of qutrit Clifford+T gates
Shai Evra, Ori Parzanchevski
The Clifford+T gate set is a topological generating set for PU(2), which has been well-studied from the perspective of quantum computation on a single qubit. The discovery that it…