发表机构
Qkrishi Quantum; North Carolina State University（Qkrishi量子; 北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对约束QAOA，提出有限深度可达集及其诊断指标$Q_R$，在207个配置中与浅层性能相关性最强（Pearson 0.7003），可作为资源受限场景的补充诊断工具。
AI 中文摘要
约束保持混合器使QAOA保持在可行子空间内，但可行性和全局混合器连通性并不能决定特定浅层电路可访问哪些可行配置。我们在实际执行的电路层面研究约束QAOA：指定可行的初始状态、有限深度和有限的混合器交互调度。我们定义了有限深度可达集$R_p(M,x_0)$，并证明理想QAOA电路的计算基支撑包含于其中。这给出了一个与参数无关的目标上限$f_R^\star=\max_{x\in R_p}f(x)$和一个归一化的可达质量诊断指标$Q_R$，将可达体积与其中包含的目标质量分离开来。我们使用资源匹配的块局部XY混合器调度对约束投资组合优化和合成块约束二次问题评估了该框架。在207个有利尾部CVaR QAOA配置中，$Q_R$与实现的浅层QAOA性能之间的关联在所考虑的结构诊断指标中最强，Pearson和Spearman相关系数分别为$0.7003$和$0.8057$；在受控和依赖感知分析下，该关系仍保持为正。这种区分在可行初始化、投资组合规模和目标函数族的变化中持续存在。一项仅编译的研究进一步表明，对于此处考虑的密集投资组合哈密顿量，相位分离器路由主导编译后的双量子比特资源规模，而具有相当编译双量子比特成本的混合器调度可能表现出显著不同的有限深度可达质量。这些结果促使将目标相关的有限深度可达性作为资源受限约束QAOA的补充诊断指标。
英文摘要
Constraint-preserving mixers keep QAOA within a feasible subspace, but feasibility and global mixer connectivity do not determine which feasible configurations are available to a particular shallow circuit. We study constrained QAOA at the level of the circuit actually executed: a specified feasible initial state, finite depth, and finite schedule of mixer interactions. We define the finite-depth accessible set $R_p(M,x_0)$ and show that the computational-basis support of the ideal QAOA circuit is contained within it. This gives a parameter-independent objective ceiling $f_R^\star=\max_{x\in R_p}f(x)$ and a normalized reachable-quality diagnostic $Q_R$, separating accessible volume from the objective quality contained within it. We evaluate this framework using resource-matched block-local XY mixer schedules for constrained portfolio optimization and synthetic block-constrained quadratic problems. Across 207 favorable-tail CVaR QAOA configurations, $Q_R$ shows the strongest association with realized shallow-QAOA performance among the structural diagnostics considered, with Pearson and Spearman correlations of $0.7003$ and $0.8057$; the relationship remains positive under controlled and dependence-aware analyses. The distinction persists across changes in feasible initialization, portfolio size, and objective family. A compilation-only study further shows that, for the dense portfolio Hamiltonians considered here, phase-separator routing dominates the compiled two-qubit resource scale, while mixer schedules with comparable compiled two-qubit cost can exhibit markedly different finite-depth accessible quality. These results motivate objective-relevant finite-depth accessibility as a complementary diagnostic for resource-bounded constrained QAOA.
Comments26 pages, 5 figures, 6 tables
