Intrinsic annealing in a hybrid memristor-magnetic tunnel junction Ising machine.

Hardware implementations of the Ising model offer promising solutions to large-scale optimization tasks. In the literature, various nanodevices have been shown to emulate the spin dynamics for such Ising machines with remarkable effectiveness. Other nanodevices have been shown to implement spin-spin coupling with compact footprint and minimal energy dissipation. However, an ideal Ising machine would associate both types of nanodevices, and they must operate synergistically to support annealing: a progressive reduction of machine stochasticity that allows it to settle to an energy minimum. Here, we report an Ising machine that combines two nanotechnologies: memristor crossbar - storing multi-level couplings - and stochastic magnetic tunnel junction (SMTJ), acting as thermally driven spins. Because the same read voltage that interrogates the crossbar also biases the SMTJs, increasing this voltage automatically lowers the effective temperature of the machine, providing an intrinsic, analog-native annealing technique. Operating at zero magnetic field, our prototype consistently reaches the global optimum of a 24-vertex weighted MAX-CUT and a 10-vertex, three-color graph-coloring problem using an externally implemented feedback loop. Given that both nanotechnologies in our demonstrator are CMOS-integrated, this approach is compatible with advanced 3D integration, offering a scalable pathway toward compact, fast, and energy-efficient large-scale Ising solvers.