PIRSA:17080006 Conference Quantum Foundations

DOI10.48660/17080006

Conference/School: Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics

Duncan, R. (2017). Introduction to CQM. Perimeter Institute. https://pirsa.org/17080006

Duncan, Ross. Introduction to CQM. Perimeter Institute, Aug. 02, 2017, https://pirsa.org/17080006 

@misc{ pirsa_PIRSA:17080006,
  doi = {10.48660/17080006},
  url = {https://pirsa.org/17080006},
  author = {Duncan, Ross},
  keywords = {Quantum Foundations, Quantum Information},
  language = {en},
  title = {Introduction to CQM},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {aug},
  note = {PIRSA:17080006 see, \url{https://pirsa.org}}
}

Abstract

Categorical quantum mechanics is a research programme which aims to axiomatise (finite dimensional) quantum theory as an algebraic theory inside an abstract symmetric monoidal category. The central idea is that quantum observables can be axiomatised as certain Frobenius algebras, and that two observables are (strongly) complementary when their Frobenius algebras jointly form a Hopf algebra. The resulting theory is surprisingly powerful, especially when combined with its graphical notation. In this talk I'll introduce the main concepts and present some applications to quantum computation.

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