Speaker
Description
This talk is based on joint work with Lachesar Georgiev and Grigory Matein, see especially JHEP 08 (2024) 084.
Fibonacci anyons provide the simplest possible model of two-sector non-Abelian fusion rules where the only non-trivial one is [1] × [1] = [0] ⊕ [1].
A conformal field theory construction of topological quantum registers and quantum gates is proposed which is based on Fibonacci anyons realized as quasi-hole excitations in a particular fractional quantum Hall state. To this end, earlier results of Ardonne and Schoutens for the correlation function of four Fibonacci fields in a $Z_3$ parafermion setting are extended to the case of arbitrary number $n$ of quasi-holes in a background of $N = 3r$ electrons.
The focus is on the braiding properties of the obtained correlators. The construction of a monodromy representation of the Artin braid group $B_n$ acting on $n$-point conformal blocks of Fibonacci anyons is explained in details. A simple recursion formula makes it possible to derive explicitly the matrices of braid group generators in block form.
Finally, we construct N qubit computational spaces in terms of conformal blocks of $2N+2$ Fibonacci anyons.