发表机构
Panasonic Holdings Corporation; The University of Osaka; Fixstars Amplify Corporation; Fixstars Corporation（松下控股公司; 大阪大学; Fixstars Amplify 公司; Fixstars 公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用模拟分岔求解器SQBM+直接优化合金高阶团簇展开哈密顿量对应的多项式无约束二元优化问题，在成分约束下高效搜索低能构型，并在Au-Cu体系中验证了方法的有效性。
AI 中文摘要
识别基态和低能原子构型是合金设计中的一个核心问题。团簇展开（CE）方法将固定晶格上的构型能量学表示为有效哈密顿量；对于二元合金，高阶CE模型成为多项式伊辛哈密顿量。以Au-Cu作为模型二元合金，我们将三次和四次团簇展开哈密顿量在固定成分约束下表述为带惩罚项的多项式无约束二元优化（PUBO）问题。我们使用SQBM+（一种基于模拟分岔的求解器，可直接处理高阶多项式二元目标）来优化这些PUBO问题。这种直接的PUBO处理避免了构建带有辅助变量的显式二次重构的需要。成分约束通过二次惩罚项施加，其权重根据CE目标连续松弛的导数系数进行估计。对多达2048个原子体系的基准计算表明，SQBM+能够稳健地获得三次CE模型的低能可行构型，并且对许多四次实例仍然有效。由优化构型构建的形成能凸包恢复了CuAu和Cu3Au的有序化趋势，并揭示了非化学计量成分下的有限尺寸效应。这些结果证明了模拟分岔是合金构型搜索中约束高阶CE优化的一条实用途径。
英文摘要
Identifying ground-state and low-energy atomic configurations is a central problem in alloy design. The cluster-expansion (CE) method represents configurational energetics on a fixed lattice as an effective Hamiltonian; for binary alloys, higher-order CE models become polynomial Ising Hamiltonians. Using Au-Cu as a model binary alloy, we formulate cubic and quartic cluster-expansion Hamiltonians as penalty-augmented polynomial unconstrained binary optimization (PUBO) problems under fixed-composition constraints. We optimize these PUBO problems using SQBM+, a simulated-bifurcation-based solver that can treat higher-order polynomial binary objectives directly. This direct PUBO treatment avoids the need to construct an explicit quadratic reformulation with auxiliary variables. Composition constraints are imposed through quadratic penalty terms, whose weights are estimated from derivative coefficients of the continuous relaxation of the CE objective. Benchmark calculations for systems up to 2048 atoms show that SQBM+ robustly obtains low-energy feasible configurations for cubic CE models and remains effective for many quartic instances. Formation-energy convex hulls constructed from the optimized configurations recover the CuAu and Cu3Au ordering trends and reveal finite-size effects at off-stoichiometric compositions. These results demonstrate simulated bifurcation as a practical route to constrained higher-order CE optimization for alloy configuration search.
Comments10 pages, 3 figures, and 1 table; Supplemental Material: 14 pages, 4 figures, and 9 tables
