Ising Hamiltonian Solver using Stochastic Phase-Transition Nano-Oscillators.

Computationally hard problems, including combinatorial optimization, can be mapped onto the problem of finding the ground-state of an Ising Hamiltonian. Thus, physical annealing systems such as Ising machines can be employed to accelerate the search for their solution. Here, we leverage the continuous-time dynamics of a network of stochastic phase-transition nano-oscillators and construct an electronic Ising Hamiltonian solver operating at room temperature. We fabricate a prototype network of capacitively coupled eight SHIL oscillators that finds the ground state of an Ising Hamiltonian and solves the maximum-cut (Max-Cut) in non-planar graphs - a problem of non-deterministic polynomial time (NP) complexity - with high probability of success. Numerical simulations are utilized to find the Max-Cut in non-planar graphs as large as 800 nodes, demonstrating up to six orders of magnitude improvement in time-to-solution and nearly ten orders of magnitude improvement in energy-to-solution compared to standard heuristic algorithms running on a state-of-the-art digital computer.