Classical simulation of Yang-Baxter gates

TitleClassical simulation of Yang-Baxter gates
Publication TypeJournal Article
Year of Publication2014
AuthorsAlagic, G, Bapat, A, Jordan, SP
Journal9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Date Published2014/07/05

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

Short Title9th Conference on the Theory of Quantum Computation