Rahul Dalal: Automorphic Representations and "Golden" Quantum Logic Gates

Any construction of a quantum computer would require finding good sets of quantum logic gates: finite sets of $2^n$-by-$2^n$ unitary matrices that efficiently and computably approximate arbitrary unitary matrices through short products. In a 2015 letter, Sarnak developed a notion of "golden" gate sets as the most efficient approximators that could reasonably be hoped for. 

We present the first proven construction of golden gates sets for $n \geq 2$ qubits, discussing the connection to the theory of automorphic representations and some key input bounds derived from the endoscopic classification. This is joint work with Shai Evra and Ori Parzanchevski.