Ising machines have emerged as a promising solution for rapidly solving NP-complete combinatorial optimization problems, surpassing the capabilities of traditional computing methods. By efficiently determining the ground state of the Hamiltonian during the annealing process, Ising machines can effectively complement CPUs in tackling optimization challenges. To realize these Ising machines, a bi-stable oscillator is essential to emulate the atomic spins and interactions of the Ising model. This study introduces a Josephson parametric oscillator (JPO)-based tile structure, serving as a fundamental unit for scalable superconductor-based Ising machines. Leveraging the bi-stable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of 7.5GHz while consuming significantly less power (by three orders of magnitude) than CMOS-based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller (LHZ) architecture ensures its viability for large-scale integration. We conducted simulations of the tile in a noisy environment to validate its functionality. We verified its operational characteristics by comparing the results with the analytical solution of its Hamiltonian model. This verification demonstrates the feasibility and effectiveness of the JPO-based tile in implementing Ising machines, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.

翻译：伊辛机已成为快速求解NP完全组合优化问题的一种有前景的解决方案，超越了传统计算方法的能力。通过在退火过程中有效确定哈密顿量的基态，伊辛机能够有效补充中央处理器应对优化挑战。为实现这些伊辛机，需要双稳态振荡器来模拟伊辛模型中的原子自旋及其相互作用。本研究引入了一种基于约瑟夫森参量振荡器（JPO）的瓦片结构，作为可扩展超导伊辛机的基本单元。利用超导振荡器JPO的双稳态特性，所提出的机器可在7.5GHz频率下运行，同时功耗比基于CMOS的系统低三个数量级。此外，所提出的瓦片结构与Lechner-Hauke-Zoller（LHZ）架构的兼容性确保了其大规模集成的可行性。我们在噪声环境下对瓦片进行了仿真以验证其功能，并通过将结果与其哈密顿量模型的解析解进行对比，验证了其运行特性。这一验证证明了基于JPO的瓦片在实现伊辛机中的可行性和有效性，为量子计算中高效且可扩展的组合优化开辟了新途径。