  We define the notion of a (linearly reductive) center for a linearly
reductive quantum group, and show that the quotient of a such a quantum group
by its center is simple whenever its fusion semiring is free in the sense of
Banica and Vergnioux. We also prove that the same is true of free products of
quantum groups under very mild non-degeneracy conditions. Several natural
families of compact quantum groups, some with non-commutative fusion semirings
and hence very "far from classical", are thus seen to be simple. Examples
include quotients of free unitary groups by their centers, recovering previous
work, as well as quotients of quantum reflection groups by their centers.
