YANG–BAXTER EQUATIONS IN QUANTUM INFORMATION

Mo‐Lin Ge, Kang Xue

Mo‐Lin Ge

Mo‐Lin Ge, Kang Xue

The connection between Yang–Baxter system and quantum information has been discussed. Based on the topological basis for both Temperley–Lieb (TL) algebra and Birman–Wenzl (BW) algebra the representations of N by N braiding matrices associated with the corresponding N2 by N2 ones are obtained. Some of physical consequences of the braiding matrices connecting with quantum information are shown.

Mo‐Lin Ge, Kang Xue, Ruo-Yang Zhang +1 more

REBECCA S. CHEN

Solutions to the Yang–Baxter equation — an important equation in mathematics and physics — and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum information science. In particular, unitary representations of the braid group are desired because they generate braiding quantum gates. These are actively studied in the ongoing research into topological quantum computing. A generalized Yang–Baxter equation was proposed a few years ago by Eric Rowell et al. By finding solutions to the generalized Yang–Baxter equation, we obtain new unitary braid group representations. Our representations give rise to braiding quantum gates and thus have the potential to aid in the construction of useful quantum computers.

P. P. Kulish

Some of main achievements obtained recently in investigations of the symmetry properties of systems solved by the quantum inverse scattering methods and connected with the Yang–Baxter equation and reflection equations are reviewed. Special attention is devoted to the twist procedure. Twist relates three constant R-matrices corresponding to Lie super-algebra gl(1|1).