Ising machines, hardware accelerators for combinatorial optimization and probabilistic sampling problems, have gained significant interest recently. A key element is stochasticity, which enables a wide exploration of configurations, thereby helping avoid local minima. Here, we refine the previously proposed concept of coupled chaotic bits (c-bits) that operate without explicit stochasticity. We show that augmenting chaotic bits with stochasticity enhances performance in combinatorial optimization, achieving algorithmic scaling comparable to probabilistic bits (p-bits). We first demonstrate that c-bits follow the quantum Boltzmann law in a 1D transverse field Ising model. We then show that c-bits exhibit critical dynamics similar to stochastic p-bits in 2D Ising and 3D spin glass models, with promising potential to solve challenging optimization problems. Finally, we propose a noise-augmented version of coupled c-bits via the adaptive parallel tempering algorithm (APT). Our noise-augmented c-bit algorithm outperforms fully deterministic c-bits running versions of the simulated annealing algorithm. Other analog Ising machines with coupled oscillators could draw inspiration from the proposed algorithm. Running replicas at constant temperature eliminates the need for global modulation of coupling strengths. Mixing stochasticity with deterministic c-bits creates a powerful hybrid computing scheme that can bring benefits in scaled, asynchronous, and massively parallel hardware implementations.

翻译：伊辛机作为组合优化与概率采样问题的硬件加速器，近年来受到广泛关注。其关键要素在于随机性，它能够广泛探索构型空间，从而帮助避免陷入局部极小值。本文中，我们改进了先前提出的无需显式随机性的耦合混沌比特（c-bits）概念。我们证明，通过为混沌比特引入随机性增强，可提升其在组合优化中的性能，实现与概率比特（p-bits）相当的算法扩展性。我们首先证明在具有横向场的伊辛模型中，c-bits遵循量子玻尔兹曼分布。随后，我们展示在二维伊辛模型与三维自旋玻璃模型中，c-bits表现出与随机p-bits相似的临界动力学行为，展现出解决复杂优化问题的潜力。最后，我们通过自适应并行回火算法（APT）提出了耦合c-bits的噪声增强版本。我们的噪声增强c-bit算法在性能上优于运行模拟退火算法变体的完全确定性c-bits。其他基于耦合振荡器的模拟伊辛机亦可从该算法中获得启发。在恒定温度下运行副本可消除对耦合强度全局调制的需求。将随机性与确定性c-bits相结合，形成了一种强大的混合计算方案，能够在规模化、异步及大规模并行硬件实现中带来显著优势。