Title: Golden Gates in PU(n) and the Density Hypothesis
Speaker: Shai Evra
Speaker Info: IAS
In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. Recently, Sarnak gave a new application of these LPS generators to the theory of theoretical quantum computations, showing that they form an excellent universal gate set for PU(2) (from both a mathematical and an algorithmic point of view). In this talk I will describe some recent works that extends the LPS construction to higher dimensional compact Lie groups.Date: Friday, November 22, 2019
A key ingredient in the work of LPS is the Ramanujan conjecture for U(2), which follows from Deligne's proof of the Ramanujan-Petersson conjecture for GL(2). Unfortunately, the naive generalization of the Ramanujan conjecture is false for higher rank groups. Following a program initiated by Sarnak in the 90's, we prove a density hypothesis and use it as a replacement of the naive Ramanujan conjecture.
This talk is based on a joint work with Ori Parzanchevski.