Ising machines are considered as promising hardware solvers. The idea is to map the solution of a problem to the ground state of an Ising spin glass and find this minimum by performing annealing in an Ising machine that emulates spin physics. However, previous approaches to deterministic sequential algorithmics have been plagued by the hiearchy problem: couplings become exponentially small along the causal direction. Here, we present a method to map sequential algorithms to an Ising problem with only a linear decay of the couplings and illustrate this with n-bit binary number adders. The resulting computing system is thus scalable, opening a way for efficient Ising machines for sequential algorithms.
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
O(1/t) annealing schedule and an
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.