Using Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

Abstract

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. GHz spin Hall nano-oscillators (SHNOs) are a particularly attractive technology for building fast, energy-efficient, and scalable Ising machines; however, electrical coupling mechanisms which allow for full programmability among different oscillator nodes have not yet been fully demonstrated in such a network. Here, we develop a general analytical framework that can describe injection locking of SHNOs with arbitrary oscillation orbits at both the fundamental frequency and harmonics. With this compact analytical framework, we integrate the SHNO into a Verilog-A device model that can emulate the oscillator’s injection locking behavior in circuit simulations, where the dynamics of coupled oscillator networks are simulated together with conventional electronic components (Fig. 1). While our abstract circuit simulations achieve similar accuracy as full micromagnetic simulations, the device model we developed leads to more than 100 times improvement in simulation efficiency and allows us to evaluate the performance using realistic circuits.Using circuit-level simulations, we further study the effects of phase noise and scalability in networks of up to hundreds of coupled oscillators to show that the SHNO-based Ising machine can be operated robustly at room temperature. Compared with existing technologies, SHNO networks exhibit orders of magnitude improvement in time, space, and energy efficiency (Table 1). Our results provide analytical tools and design insights that will be useful for the realization of a CMOS-integrated SHNO Ising machine.  Fig. 1: (a) Electrical coupling circuit linking two SHNOs in the oscillator-based Ising machine. (b) Phases of oscillators in a 4-node coupled network solving the Ising model in circuit simulations (HSPICE) using our abstract device model and in micromagnetic simulations (MuMax3).  Table 1: Comparison of speed, energy, and space metrics between the SHNO Ising machine and existing technologies. Values are standardized to a 100-node network.