Noise-augmented Chaotic Ising Machines for Combinatorial Optimization and Sampling

Kyle Lee, Shuvro Chowdhury, Kerem Y. Camsari
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Abstract

The rise of domain-specific computing has led to great interest in Ising machines, dedicated hardware accelerators tailored to solve combinatorial optimization and probabilistic sampling problems. A key element of Ising machines is stochasticity, which enables a wide exploration of configurations, thereby helping avoid local minima. Here, we evaluate and improve the previously proposed concept of coupled chaotic bits (c-bits) that operate without any explicit stochasticity. We show that augmenting chaotic bits with stochasticity leads to better algorithmic scaling in combinatorial optimization problems, comparable to the performance of probabilistic bits (p-bits) which have explicit randomness in their update rules. We first demonstrate that c-bits surprisingly follow the quantum Boltzmann law in a 1D transverse field Ising model, despite the lack of explicit randomness. We then show that c-bits exhibit critical dynamics similar to those of 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 powerful adaptive parallel tempering algorithm (APT). The noise-augmented c-bit algorithm outperforms fully deterministic c-bits running versions of the simulated annealing algorithm. Chaotic Ising machines closely resemble coupled oscillator-based Ising machines, as both schemes exploit nonlinear dynamics for computation. Oscillator-based Ising machines may greatly benefit from our proposed algorithm, which runs replicas at constant temperature, eliminating the need to globally modulate 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.
用于组合优化和采样的噪声增强混沌伊辛机
随着特定领域计算的兴起,人们对专门用于解决组合优化和概率采样问题的专用硬件加速器 Isingmachines 产生了浓厚兴趣。随机性是 Isingmachines 的一个关键要素,它可以广泛探索各种配置,从而帮助避免局部最小值。在此,我们对之前提出的耦合混沌比特(c-bits)概念进行了评估和改进。我们的研究表明,在组合优化问题中,用随机性增强混沌比特能带来更好的算法扩展,其性能可与在更新规则中具有显式随机性的概率比特(p-bits)相媲美。我们首先证明,尽管没有明确的随机性,但在一维横向场兴模型中,c 位出人意料地遵循量子波尔兹曼定律。然后,我们证明了 c-bit 在二维伊辛模型和三维自旋玻璃模型中表现出与随机 p-bit 类似的临界动力学,有望解决具有挑战性的优化问题。最后,我们通过功能强大的自适应并行回火算法(APT),提出了耦合 c-bit 的噪声增强版本。噪声增强 c 位算法优于运行模拟退火算法版本的完全确定性 c 位算法。混沌伊辛机与基于振荡器的耦合伊辛机非常相似,因为这两种方案都利用非线性动力学进行计算。我们提出的算法在恒定温度下运行副本,无需全局调节耦合强度,因此基于振荡器的伊兴机可以从我们的算法中受益匪浅。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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