2026-07-22T18:56:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4814 2024-03-06T10:35:12Z ddc:004 open_access

Classical Simulation of Yang-Baxter Gates Alagic, Gorjan Bapat, Aniruddha Jordan, Stephen Quantum Yang-Baxter Braid Anyon 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Gorjan Alagic and Aniruddha Bapat and Stephen Jordan 2014 Is Part Of LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2014.161 urn:nbn:de:0030-drops-48143 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.161 eng https://creativecommons.org/licenses/by/3.0/legalcode