10 citations · 28 across the 11 of their papers we have counts for
13 papers
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…
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…
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…
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…
Good Locally Testable Codes
Irit Dinur, Shai Evra, Ron Livne +2
An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the -problem.
Locally Testable Codes with constant rate, distance, and locality
Irit Dinur, Shai Evra, Ron Livne +2
A locally testable code (LTC) is an error-correcting code that has a property-tester. The tester reads bits that are randomly chosen, and rejects words with probability proport…
Decodable quantum LDPC codes beyond the distance barrier using high dimensional expanders
Shai Evra, Tali Kaufman, Gilles Zémor
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we…
Ramanujan complexes and Golden Gates in PU(3)
Shai Evra, Ori Parzanchevski
In a seminal series of papers from the 80's, Lubotzky, Phillips and Sarnak applied the Ramanujan-Petersson Conjecture for (Deligne's theorem), to a special family of arith…
Good cyclic codes and the uncertainty principle
Shai Evra, Emmanuel Kowalski, Alexander Lubotzky
A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The…
Bounded Degree Cosystolic Expanders of Every Dimension
Shai Evra, Tali Kaufman
In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan c…
Finite quotients of Bruhat-Tits buildings as geometric expanders
Shai Evra
In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes h…
Mixing properties and the chromatic number of Ramanujan complexes
Shai Evra, Konstantin Golubev, Alexander Lubotzky
Ramanujan complexes are high dimensional simplical complexes generalizing Ramanujan graphs. A result of Oh on quantitative property (T) for Lie groups over local fields is used to…