量子启发式求解器中一般阶伊辛类哈密顿量的约化方案
A reduction scheme for general-order Ising-like Hamiltonians in quantum heuristic solvers
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中文总结 AI 辅助
针对伊辛模型求解难问题，将不可分离组概念推广到任意阶伊辛类模型，开发哈密顿量约化框架，通过迭代检测合并受约束自旋组为单变量，在合成超图等数据集上测试并评估其与下游流程集成，为高阶伊辛类优化问题约化奠定基础。
中文摘要 AI 辅助
伊辛模型在各种优化问题中普遍存在，但因组合爆炸难以求解。哈密顿量约化是应用启发式求解器前减小有效问题规模的有用预处理技术。现有技术主要针对二阶伊辛模型，而许多伪布尔公式自然包含高阶相互作用。本文将不可分离组概念推广到任意阶伊辛类模型，开发了一个哈密顿量约化框架，通过迭代检测并将受约束自旋组合并为单个变量。我们在合成超图和高阶网络数据集上对约化进行基准测试，并评估其与下游降阶和求解器工作流程的集成。结果为高阶伊辛类优化问题的哈密顿量约化奠定了基础。
英文摘要
The Ising model is ubiquitous in various optimization problems but notoriously difficult to solve due to combinatorial explosion. In view of this, Hamiltonian reduction is a useful preprocessing technique for reducing the effective problem size before applying heuristic solvers. However, existing reduction techniques mainly target second-order Ising models, whereas many pseudo-Boolean formulations naturally contain higher-order interactions. In this work, we generalize the concept of non-separable groups to arbitrary-order Ising-like models and develop a Hamiltonian reduction framework that iteratively detects and merges constrained spin groups into single variables. We benchmark the reduction on synthetic hypergraphs and higher-order network datasets, and evaluate its integration with downstream order-reduction and solver workflows. Our results establish a foundation for Hamiltonian reduction in higher-order Ising-like optimization problems.
