arXiv:2304.00710

Universal Braiding Quantum Gates

David Lovitz

Published Apr 3, 2023• 0 citations

Abstract

The Yang-Baxter equation and it's various forms have applications in many fields, including statistical mechanics, knot theory, and quantum information. Unitary solutions of the braided Yang-Baxter equation are of particular interest as quantum gates for topological quantum computers. We demonstrate a simple construction for solutions in any dimension, which are both unitary and universal for quantum computation. We also fully classify a family of solutions to certain generalized Yang-Baxter equations and prove that certain instances of the equation only have solutions that are scalar multiples of the identity.

DOI: 10.48550/arxiv.2304.00710

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