Universal quantum computation with metaplectic anyons

Wang, Zhenghan

doi:10.1063/1.4914941

Title: Universal quantum computation with metaplectic anyons

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Abstract

We show that braidings of the metaplectic anyons X{sub ϵ} in SO(3){sub 2} = SU(2){sub 4} with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p){sub 2} for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.

Authors:

Wang, Zhenghan ^[1]

Department of Mathematics, University of California, Santa Barbara, California 93106 (United States)

Publication Date:: Sun Mar 15 00:00:00 EDT 2015

OSTI Identifier:: 22403120

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANYONS; LIE GROUPS; QUANTUM COMPUTERS; QUANTUM MECHANICS; SIMULATION

Citation Formats


                    Cui, Shawn X., E-mail: xingshan@math.ucsb.edu, Wang, Zhenghan, and Microsoft Research Station Q, University of California, Santa Barbara, California 93106. Universal quantum computation with metaplectic anyons.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4914941.

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                    Cui, Shawn X., E-mail: xingshan@math.ucsb.edu, Wang, Zhenghan, & Microsoft Research Station Q, University of California, Santa Barbara, California 93106. Universal quantum computation with metaplectic anyons.  United States.  https://doi.org/10.1063/1.4914941

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                    Cui, Shawn X., E-mail: xingshan@math.ucsb.edu, Wang, Zhenghan, and Microsoft Research Station Q, University of California, Santa Barbara, California 93106. 2015.  
        "Universal quantum computation with metaplectic anyons".  United States.  https://doi.org/10.1063/1.4914941.

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@article{osti_22403120,

  title        = {Universal quantum computation with metaplectic anyons},

  author       = {Cui, Shawn X., E-mail: xingshan@math.ucsb.edu and Wang, Zhenghan and Microsoft Research Station Q, University of California, Santa Barbara, California 93106},

  abstractNote = {We show that braidings of the metaplectic anyons X{sub ϵ} in SO(3){sub 2} = SU(2){sub 4} with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p){sub 2} for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.},

  doi          = {10.1063/1.4914941},

  url          = {https://www.osti.gov/biblio/22403120},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 3,

  volume       = 56,

  place        = {United States},

  year         = {Sun Mar 15 00:00:00 EDT 2015},

  month        = {Sun Mar 15 00:00:00 EDT 2015}

}

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