The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. In this talk, I will discuss how an electrically coupled array of gigahertz spin Hall nano-oscillators can realize such a network (1). By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, I will explicitly show the mapping between the coupled oscillators’ physical properties and the Ising model. I will describe how our analytical model is integrated into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillator networks at the circuit level using conventional electronic components and considering phase noise and scalability. Finally, I will demonstrate how our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency.

References:

1. B. C. McGoldrick, J. Z. Sun, and L. Liu, Physical Review Applied, Vol. 17 (1), p.014006 (2022).
   
2. J. Chou, S. Bramhavar, S. Ghosh, et. al., Scientific Reports, Vol. 9 (1), p.1 (2019).