Universal Braiding Quantum Gates
Quantum Physics
2023-04-04 v1 Geometric Topology
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.
Cite
@article{arxiv.2304.00710,
title = {Universal Braiding Quantum Gates},
author = {David Lovitz},
journal= {arXiv preprint arXiv:2304.00710},
year = {2023}
}