  Classical or quantum physical systems can simulate the Ising Hamiltonian for
large-scale optimization and machine learning. However, devices such as quantum
annealers and coherent Ising machines suffer an exponential drop in the
probability of success in finite-size scaling. We show that by exploiting high
dimensional embedding of the Ising Hamiltonian and subsequent dimensional
annealing, the drop is counteracted by an exponential improvement in the
performance. Our analysis relies on extensive statistics of the convergence
dynamics by high-performance computing. We propose a realistic experimental
implementation of the new annealing device by off-the-shelf coherent Ising
machine technology. The hyperscaling heuristics can also be applied to other
quantum or classical Ising machines by engineering nonlinear gain, loss, and
non-local couplings.
