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The Ising machine is an unconventional computing architecture that can beused to solve NP-hard combinatorial optimization problems more efficiently thantraditional von Neumann architectures. Fast, compact oscillator networks whichprovide programmable connectivities among arbitrary pairs of nodes are highlydesirable for the development of practical oscillator-based Ising machines.Here we propose using an electrically coupled array of GHz spin Hallnano-oscillators to realize such a network. By developing a general analyticalframework that describes injection locking of spin Hall oscillators with largeprecession angles, we explicitly show the mapping between the coupledoscillators' properties and the Ising model. We integrate our analytical modelinto a versatile Verilog-A device that can emulate the coupled dynamics of spinHall oscillators in circuit simulators. With this abstract model, we analyzethe performance of the spin Hall oscillator network at the circuit level usingconventional electronic components and considering phase noise and scalability.Our results provide design insights and analysis tools toward the realizationof a CMOS-integrated spin Hall oscillator Ising machine operating with a highdegree of time, space, and energy efficiency.

Ising Machine Based on Electrically Coupled Spin Hall Nano-Oscillators