标题： 用于组合优化的非二进制动力学伊辛机 显示英文标题

标题： Non-binary dynamical Ising machines for combinatorial optimization

摘要： 动态伊辛机通过将经典自旋网络达到基态的收敛过程映射到特制的连续动力系统的演化上来，从而加速解决复杂的组合优化问题。 构建此类系统的主要适应原则基于以下要求：一方面，系统收敛到二元状态；另一方面，系统在这种状态下的能量模仿经典的伊辛哈密顿量。 二元类似状态的出现被认为是动态伊辛机不可或缺的特征，因为它建立了机器的连续终端状态与组合优化问题固有的离散解之间的关系。 这一点在未知量由自旋复合体表示的问题中尤为突出，例如图着色问题。 在这种情况下，连续状态到自旋构型的不精确映射可能导致需要大量后处理的无效解。 与这种方法相反，我们展示了存在一类非二元动态伊辛机，其状态的连续性与自旋状态的离散性之间不存在不一致。 我们通过将此类机器应用于寻找适当的图着色、构造拉丁方和解决数独问题来展示这一特性。 因此，我们证明了表征离散状态的信息可以在本质上连续的动力系统中明确呈现。 这为实现可扩展的组合优化电子加速器开辟了新的机会。 显示英文摘要

摘要： Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous dynamical systems. The main adapted principle of constructing such systems is based on requiring that, on the one hand, the system converges to a binary state and, on the other hand, the system's energy in such states mimics the classical Ising Hamiltonian. The emergence of binary-like states is regarded to be an indispensable feature of dynamical Ising machines as it establishes the relation between the machine's continuous terminal state and the inherently discrete solution of a combinatorial optimization problem. This is emphasized by problems where the unknown quantities are represented by spin complexes, for example, the graph coloring problem. In such cases, an imprecise mapping of the continuous states to spin configurations may lead to invalid solutions requiring intensive post-processing. In contrast to such an approach, we show that there exists a class of non-binary dynamical Ising machines without the incongruity between the continuous character of the machine's states and the discreteness of the spin states. We demonstrate this feature by applying such a machine to the problems of finding proper graph coloring, constructing Latin squares, and solving Sudoku puzzles. Thus, we demonstrate that the information characterizing discrete states can be unambiguously presented in essentially continuous dynamical systems. This opens new opportunities in the realization of scalable electronic accelerators of combinatorial optimization.