We suggest and demonstrate an all-optical quantum simulator for
single-qubit noisy channels originating from the interaction with a
fluctuating field. The simulator employs the polarization degree of
freedom of a single photon and exploits its spectral components to
average over the realizations of the stochastic dynamics. As a proof of
principle, we run simulations of dephasing channels driven either by
Gaussian (Ornstein-Uhlenbeck) or non-Gaussian (random telegraph)
stochastic processes.