Generalized Yang-Baxter equations and braiding quantum gates (Q2890234)

As well known, to derive his famous solution of the Ising model, Onsager employed so called star-triangle transformation which is known as the Yang-Baxter equation. To examine this, very important equation in both mathematics and physics, widely applied, throughout the afforded braid group representations of the solutions of this equation, in knot theory, statistical mechanics, and quantum information, constitutes the key goal of this work. The latter layout is the following. The generalization of the Yang-Baxter equation (GYBE) is reviewed in Section 2. In Section 3, the authors propose new solutions of the GYBE and in Section 4 they derive new unitary braid group representations. The last Section is left for the discussion of some open problems and future perspectives.