A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group Bn 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.
9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
, Alagic, G.
and Bapat, A.
Classical simulation of Yang-Baxter gates, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014), Singapore, -1
(Accessed December 7, 2023)