Automorphic Representations and Quantum Logic Gates

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Meeting ID: 588 829 0849
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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.