TY - JOUR
T1 - Classical simulation of Yang-Baxter gates
JF - 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Y1 - 2014
A1 - Gorjan Alagic
A1 - Aniruddha Bapat
A1 - Stephen P. Jordan
AB - 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.
VL - 27
U4 - 161-175
UR - http://arxiv.org/abs/1407.1361v1
J1 - 9th Conference on the Theory of Quantum Computation
U5 - 10.4230/LIPIcs.TQC.2014.161
ER -