  We study the dynamics of bosonic and fermionic anyons defined on a
one-dimensional lattice, under the effect of Hamiltonians quadratic in creation
and annihilation operators, commonly referred to as linear optics. These
anyonic models are obtained from deformations of the standard bosonic or
fermionic commutation relations via the introduction of a non-trivial exchange
phase between different lattice sites. We study the effects of the anyonic
exchange phase on the usual bosonic and fermionic bunching behaviors. We show
how to exploit the inherent Aharonov-Bohm effect exhibited by these particles
to build a deterministic, entangling two-qubit gate and prove quantum
computational universality in these systems. We define coherent states for
bosonic anyons and study their behavior under two-mode linear-optical devices.
In particular we prove that, for a specific value of the exchange factor, an
anyonic mirror can generate cat states, an important resource in quantum
information processing with continuous variables.
