PIRSA:08040065

Yang-Baxter Equations, Extra-special Two-groups and Topological-like Features in Quantum Information Theory

Wu, Y. (2008). Yang-Baxter Equations, Extra-special Two-groups and Topological-like Features in Quantum Information Theory . Perimeter Institute. https://pirsa.org/08040065

Wu, Yong-Shi. Yang-Baxter Equations, Extra-special Two-groups and Topological-like Features in Quantum Information Theory . Perimeter Institute, Apr. 29, 2008, https://pirsa.org/08040065 

          @misc{ pirsa_PIRSA:08040065,
            doi = {10.48660/08040065},
            url = {https://pirsa.org/08040065},
            author = {Wu, Yong-Shi},
            keywords = {Quantum Information},
            language = {en},
            title = {Yang-Baxter Equations, Extra-special Two-groups and Topological-like Features in Quantum Information Theory },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {apr},
            note = {PIRSA:08040065 see, \url{https://pirsa.org}}
          }

Yong-Shi Wu University of Utah

DOI 10.48660/08040065
Collection
Talk Type Conference
Subject

Abstract

Recently a simple but perhaps profound connection has been observed between the unitary solutions of the Yang-Baxter Equations (YBE) and the entangled Bell states and their higher dimensional (or more-qubit) extensions, the generalized GHZ states. We have shown that this connection can be made more explicit by exploring the relation between the solutions of the YBE and the representations of the extra-special two-groups. This relationship brings certain topological-like features to quantum information theory, and makes a connection to the well-known Jones polynomials which are topological invariants of knots and links. This emerging connection may deepen our understanding, through new representations of extra-special two-groups, of quantum error correction and topological quantum computation. This work is a collaboration with Eric Rowell, Zhenghan Wang, Molin Ge, and Yong-Zhang.