Classical simulation of YangBaxter gates
Abstract
A unitary operator that satisfies the constant YangBaxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantumcomputational 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 YangBaxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 DOI:
 10.48550/arXiv.1407.1361
 arXiv:
 arXiv:1407.1361
 Bibcode:
 2014arXiv1407.1361A
 Keywords:

 Quantum Physics;
 Mathematics  Quantum Algebra
 EPrint:
 17 pages. Corrected error in proof of Theorem 1