Braiding Fibonacci anyons

Abstract

Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle excitations in the Z_3 parafermion fractional quantum Hall state. To this end, the results of Ardonne and Schoutens for the correlation function of n = 4 Fibonacci fields are extended to the case of arbitrary n (and 3 r electrons). Special attention is paid to the braiding properties of the obtained correlators. We explain in details the construction of a monodromy representation of the Artin braid group acting on n-point conformal blocks of Fibonacci anyons. For low n (up to n = 8), the matrices of braid group generators are displayed explicitly. A simple recursion formula makes it possible to extend without efforts the construction to any n. Finally, we construct N qubit computational spaces in terms of conformal blocks of 2N + 2 Fibonacci anyons.

minor revisions (39 pages, 3 figures)

References in corpus (7)

• Braid Topologies for Quantum Computation
• Quantum groups and nonabelian braiding in quantum Hall systems
• Parafermion Hall states from coset projections of abelian conformal theories
• Topological Quantum Compiling
• Wavefunctions for topological quantum registers
• Ising-like and Fibonacci-Anyons from KZ-equations
• Monodromy Representations of the Braid Group

Cited by in corpus (1)

• Measuring Chern-Simons level $k$ by braiding $SU(2{)}_k$ anyons