Yan-Ting LiuChih-Chen PengTzu-Yen HungYu-Hao HuangCHI-FENG PAI2024-12-242024-12-242024-12-02https://www.scopus.com/record/display.uri?eid=2-s2.0-85211007814&origin=resultslisthttps://scholars.lib.ntu.edu.tw/handle/123456789/724345Addressing combinatorial optimization problems (COPs) using conventional computational approaches is often resource intensive in terms of time and power consumption. The oscillator-based Ising machine, which combines oscillator units with the Ising model, presents a promising avenue for efficiently solving COPs. In this context, we explore the viability of leveraging self-sustained magnetic oscillations, specifically the spin Hall nano-oscillator (SHNO), to establish an electrically coupled oscillator Ising machine. To evaluate the potential applications of such Ising machines, we theoretically construct networks of SHNOs and deploy them to address two prevalent COPs: the max-cut problem and the traveling salesman problem (TSP). For the max-cut problem, we propose an optimized annealing schedule that can significantly enhance the success probability of finding the optimal solution. In the case of the TSP, we showcase the capability of the SHNO-based Ising machine to address this problem by introducing a Zeeman coupling term to account for penalty considerations, along with a suitable normalization strategy to effectively incorporate distance-related issues inherent in the TSP. Our study offers comprehensive investigations into the coupled SHNO networks, providing insights for the design and the development of unconventional computing architectures based on SHNOs for quantum-inspired applications.falsejournal article10.1103/PhysRevApplied.22.0640092-s2.0-85211007814