Higher-order neuromorphic Ising machines—autoencoders and Fowler-Nordheim annealers are all you need for scalability

We report that an autoencoder-based neuromorphic architecture, combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. We show that these machines can consistently produce state-of-the-art solutions with high reliability and with competitive time-to-solution metrics. The autoencoder captures higher-order interactions by decomposing Ising clauses and Ising spins into encoder-decoder layers of spiking neurons, thereby keeping the resource complexity independent of the interaction order for sparse problems. An annealing process based on the dynamics of Fowler-Nordheim quantum mechanical tunneling extrapolates between an $${{\mathcal{O}}}(1/t)$$ annealing schedule and an $${{\mathcal{O}}}(1/\log (t))$$ annealing schedule. This not only ensures fast convergence towards high-quality solutions but also guarantees asymptotic convergence to the Ising ground state. To demonstrate the advantages of the proposed higher-order neuromorphic Ising machine, we systematically solved benchmark combinatorial optimization problems such as MAX-CUT and MAX-SAT, comparing the results to those obtained using a second-order Ising machine employing the same annealing process. The authors demonstrate that an autoencoder-based neuromorphic architecture combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. They show that these machines can consistently produce state-of-the-art solutions with high reliability and competitive time-to-solution metrics.