Classical simulation of Yang-Baxter gates

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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.

Citation

Alagic, G., Bapat, A., & Jordan, S. (2014, November). “Classical Simulation of Yang-Baxter Gates”. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (p. 161).

  @article{alagic2014,
  author = {Gorjan Alagic and Aniruddha Bapat and Stephen P Jordan},
  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 = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014), Leibniz International Proceedings in Informatics (LIPIcs)},
  year = {2014},
  volume = {27},
  publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  doi =  {10.4230/LIPIcs.TQC.2014.161},
}