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From high dimensional expanders to quantum computation

Algebra & Discrete Mathematics

Speaker: Ori Parzanchevski, Hebrew U in Jerusalem
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Location: Zoom lecture
Start time: Thu, Dec 10 2020, 10:00AM

In a series of papers from the eighties, Lubotzky, Phillips, and Sarnak used number theory to construct optimally expanding graphs (which are known as Ramanujan graphs), and optimal topological generators for the group SO(3). Recently, it was observed that these topological generators are useful in quantum computation, since SO(3) is isomorphic to PU(2), the group of logical gates on a single qubit. In joint works with Sarnak and Evra, we generalize these ideas to higher dimensions. On the discrete side, we use affine buildings to obtain Ramanujan complexes, which are simplicial complex analogues of Ramanujan graphs. On the continuous side, we obtain logical gates on more than one qubit. I will give a survey of these results with a broad audience in mind.

All meetings this quarter will be by Zoom. Please see announcements or contact organizers for the passcode.

Stay afterwards for a brief, informal reception. Refreshments will be self-provided.