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IQI Weekly Seminar

Tuesday, September 8, 2020
1:00pm to 2:00pm
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The representation theory of the Clifford group, with sundry applications
David Gross, Professor of Physics, University of Cologne,

Abstract: I will report on an ongoing project to work out and exploit an analogue of Schur-Weyl duality for the Clifford group. Schur-Weyl establishes a one-one correspondence between irreps of the unitary group and those of the symmetric group. A similar program can be carried out for Cliffords. The permutations are then replaced by certain discrete orthogonal maps. As is the case for Schur-Weyl, this duality has many applications for
problems in quantum information. It can be used, e.g., to derive quantum property tests for stabilizerness and Cliffordness, bounds on stabilizer rank, the construction of designs using few non-Clifford resources, and
many more.

[arXiv:2002.09524, 1906.07230, 1712.08628]

For more information, please contact Bonnie Leung by email at bjleung@caltech.edu.