Braiding operators are universal quantum gates

  title={Braiding operators are universal quantum gates},
  author={Louis H. Kauffman and Samuel J. Lomonaco},
  journal={New Journal of Physics},
This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix)oftheYang-Baxterequationisauniversalgateforquantumcomputing,in thepresenceoflocalunitarytransformations.Weshowthatthissame Rgeneratesa new non-trivial invariant of braids, knots and links. Other solutions of theYang- Baxter equation are also shown to be universal for quantum computation. The… Expand
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