  Networks of nonlinear parametric resonators are promising candidates as Ising
machines for annealing and optimization. These many-body out-of-equilibrium
systems host complex phase diagrams of coexisting stationary states. The
plethora of states manifest via a series of bifurcations, including
bifurcations that proliferate purely unstable solutions, which we term ``ghost
bifurcations''. Here, we demonstrate that the latter take a fundamental role in
the stochastic dynamics of the system in the presence of noise. Specifically,
they determine the switching paths and the switching rates between stable
solutions. We demonstrate experimentally the impact of ghost bifurcations on
the noise-activated switching dynamics in a network of two coupled parametric
resonators.

Classical Physics