Ising Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

Abstract

The Ising machine is an unconventional computing architecture that can solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann computing architectures. The spin Hall nano-oscillator has potential as a building block for a high-speed, low-power Ising machine based on its GHz operating frequency, sub-micron dimensions, and high degree of tunability. We develop an analytical framework describing how the dynamics of an electrically coupled array of spin Hall oscillators can be mapped to the Ising Hamiltonian based on the device characteristics. Our analytical model is integrated into a lightweight and versatile Verilog-A device that is used to model the nonlinear spin Hall oscillator’s phase dynamics in SPICEbased circuit simulators. Finally, by integrating this device model with off-the-shelf electronic amplifier models, we analyze the Ising machine performance at the circuit level considering phase noise and scalability of the coupled network. The physics-based analytical models and quantitative tools presented in this work will enable future experimental realization of an electrically coupled spin Hall oscillator-based Ising machine operating with a high degree of time, space, and energy efficiency.