Automorphic Representations and Quantum Logic Gates (joint seminar with UBC)
Rahul Dalal (University of Vienna)
Abstract: Any construction of a quantum computer requires finding a good set of universal quantum logic gates: abstractly, a finite set of matrices in U(2^n) such that short products of them can efficiently approximate arbitrary unitary transformations. The 2-qubit case n=2 is of particular practical interest. I will present the first construction of an optimal, so-called "golden" set of 2-qubit gates.
The modern theory of automorphic representations on unitary groups---in particular, the endoscopic classification and higher-rank versions of the Ramanujan bound---will play a crucial role in proving the necessary analytic estimate: specifically, a weight-aspect variant of the density hypothesis first considered by Sarnak and Xue.
algebraic geometrynumber theory
Audience: researchers in the discipline
Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).
We acknowledge the support of PIMS, NSERC, and SFU.
For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.
We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca
| Organizer: | Katrina Honigs* |
| *contact for this listing |