PIRSA:08040060

Emergence of non-abelian statistics from an abelian model

Pachos, J. (2008). Emergence of non-abelian statistics from an abelian model. Perimeter Institute. https://pirsa.org/08040060

Pachos, Jiannis. Emergence of non-abelian statistics from an abelian model. Perimeter Institute, Apr. 30, 2008, https://pirsa.org/08040060 

          @misc{ pirsa_PIRSA:08040060,
            doi = {10.48660/08040060},
            url = {https://pirsa.org/08040060},
            author = {Pachos, Jiannis},
            keywords = {Quantum Information},
            language = {en},
            title = {Emergence of non-abelian statistics from an abelian model},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {apr},
            note = {PIRSA:08040060 see, \url{https://pirsa.org}}
          }

Jiannis Pachos University of Leeds

DOI 10.48660/08040060
Collection
Talk Type Conference
Subject

Abstract

It is well known that the toric code model supports abelian anyons. It can be realized on a square lattice of qubits, where the anyons are represented by the endpoints of strings of Pauli operators. We will demonstrate that the non-abelian Ising model can be realized in a similar way, where now the string operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code ones, reproducing the required fusion, braiding and statistical properties. We propose a string framing and ancillary qubits to implement the non-trivial chirality of this model.