Anyon computers with smaller groups

Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons based on finite groups that are solvable but not nilpotent are capable of universal quantum computation. This extends previously published results to groups that are smaller, and therefore more practical. Additionally, a new universal gate-set is built out of an operation called a probabilistic projection, and a quasi-universal leakage correction scheme is discussed.