AI 中文总结
针对人员排班问题，开发约束保持 QAOA 框架，将硬调度约束嵌入混合哈密顿量，从转移图角度制定动力学并引入受保护 XY 混合器，通过紧密模式扩展优化，能消除惩罚校准，保证可行演化，输出高质量分布。
AI 中文摘要
量子近似优化算法（QAOA）是用于组合优化的一个有前景的框架，但约束问题通常使用能量惩罚项处理，这需要校准且允许不可行配置动态可达。我们为人员排班开发了一个约束保持 QAOA 框架，将硬调度约束直接嵌入混合哈密顿量。使用具有每日覆盖和无连续值班约束的二元排班模型，从转移图角度制定动力学并引入受保护 XY 混合器，将演化限制在完全可行的调度流形。进一步区分可行性保持和可行转移设计，提出紧密模式扩展。精确态矢模拟表明，与惩罚 -X 和覆盖 -XY 公式相比，该方法消除硬约束惩罚校准，保证构造上的可行演化，且始终产生更高质量输出分布，更集中于最优可行调度。据我们所知，这是首个用于人员排班的约束保持 QAOA 公式，转移图框架易于应用于广泛的约束量子优化问题。
英文摘要
The Quantum Approximate Optimization Algorithm (QAOA) is a promising framework for combinatorial optimization, but constrained problems are commonly handled using energetic penalty terms that require calibration and allow infeasible configurations to remain dynamically accessible. We develop a constraint-preserving QAOA framework for personnel rostering in which hard scheduling constraints are embedded directly into the mixer Hamiltonian. Using a binary rostering model with daily coverage and no-consecutive-duty constraints, we formulate the dynamics from a transition-graph perspective and introduce a guarded-XY mixer that confines the evolution to the fully feasible scheduling manifold. We further distinguish feasibility preservation from feasible-transition design and propose a tight-pattern extension that introduces collective feasible exchanges in saturated workload segments where local guarded exchanges alone are insufficient. Exact statevector simulations demonstrate that, compared with Penalty-X and Coverage-XY formulations under both expectation-value and Conditional Value-at-Risk optimization, the proposed approach eliminates hard-constraint penalty calibration, guarantees feasible evolution by construction, and consistently yields higher-quality output distributions with stronger concentration on optimal feasible schedules. To the best of our knowledge, this is the first constraint-preserving QAOA formulation for personnel rostering, and the transition-graph framework is readily applicable to a broad class of constrained quantum optimization problems.
