PIRSA:19110141 Conference Quantum Information

DOI10.48660/19110141

Conference/School: Symmetry, Phases of Matter, and Resources in Quantum Computing

Gross, D. (2019). The representation theory of the Clifford group, with applications to resource theories. Perimeter Institute. https://pirsa.org/19110141

Gross, David. The representation theory of the Clifford group, with applications to resource theories. Perimeter Institute, Nov. 28, 2019, https://pirsa.org/19110141 

@misc{ pirsa_PIRSA:19110141,
  doi = {10.48660/19110141},
  url = {https://pirsa.org/19110141},
  author = {Gross, David},
  keywords = {Quantum Information},
  language = {en},
  title = {The representation theory of the Clifford group, with applications to resource theories},
  publisher = {Perimeter Institute},
  year = {2019},
  month = {nov},
  note = {PIRSA:19110141 see, \url{https://pirsa.org}}
}

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, a new direct interpretation of the sum-negativity of Wigner functions, bounds on stabilizer rank, the construction of designs using few non-Clifford resources, etc. [arXiv:1609.08172, arXiv:1712.08628, arXiv:1906.07230, arXiv:out.soon].

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