  The vision of building computational hardware for problem optimization has
spurred large efforts in the physics community. In particular, networks of Kerr
parametric oscillators (KPOs) are envisioned as simulators for finding the
ground states of Ising Hamiltonians. It was shown, however, that KPO networks
can feature large numbers of unexpected solutions that are difficult to sample
with the existing deterministic (i.e., adiabatic) protocols. In this work, we
experimentally realize a system of two classical coupled KPOs, and we find good
agreement with the predicted mapping to Ising states. We then introduce a
protocol based on stochastic sampling of the system, and we show how the
resulting probability distribution can be used to identify the ground state of
the corresponding Ising Hamiltonian. This method is akin to a Monte Carlo
sampling of multiple out-of-equilibrium stationary states and is less prone to
become trapped in local minima than deterministic protocols.
