  Parafermionic zero modes are fractional topologically protected
quasiparticles expected to arise in various platforms. We show that Coulomb
charging effects define a parafermion box with unique access options via
fractional edge states and/or quantum antidots. Basic protocols for the
detection, manipulation, and control of parafermionic quantum states are
formulated. With those tools, one may directly observe the dimension of the
zero-mode Hilbert space, prove the degeneracy of this space, and perform
on-demand digital operations satisfying a parafermionic algebra.
