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DOI: 10.4230/LIPIcs.TQC.2014.161

Classical Simulation of Yang-Baxter Gates

Authors: Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B_n for every n >= 2. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., d = 2) solutions, and some simple families that include solutions for arbitrary d >= 2. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting.

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Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan. Classical Simulation of Yang-Baxter Gates. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 161-175, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{alagic_et_al:LIPIcs.TQC.2014.161,
  author =	{Alagic, Gorjan and Bapat, Aniruddha and Jordan, Stephen},
  title =	{{Classical Simulation of Yang-Baxter Gates}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{161--175},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.161},
  URN =		{urn:nbn:de:0030-drops-48143},
  doi =		{10.4230/LIPIcs.TQC.2014.161},
  annote =	{Keywords: Quantum, Yang-Baxter, Braid, Anyon}
}

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Classical Simulation of Yang-Baxter Gates

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