01280nas a2200157 4500008004100000245004600041210004500087260001500132300001200147490000700159520085500166100001901021700002101040700002401061856003701085 2014 eng d00aClassical simulation of Yang-Baxter gates0 aClassical simulation of YangBaxter gates c2014/07/05 a161-1750 v273 a A unitary operator that satisfies the constant Yang-Baxter 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 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 $d \ge 2$. 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.
1 aAlagic, Gorjan1 aBapat, Aniruddha1 aJordan, Stephen, P. uhttp://arxiv.org/abs/1407.1361v1