We study finite-layer alternations of the \emph{Constraint--Enhanced Quantum Approximate Optimization Algorithm} (CE--QAOA), a constraint-aware ansatz that operates natively on block one-hot manifolds. Our focus is on feasibility and optimality guarantees. We show that restricting cost angles to a harmonic lattice exposes a positive Fejér filter acting on the cost-phase unitary $U_C(γ)=e^{-iγH_C}$ \emph{in a cost-dephased reference model (used only for analysis)}. Under a wrapped phase-separation condition, this yields \emph{dimension-free} finite-depth and finite-shot lower bounds on the success probability of sampling an optimal solution. In particular, we obtain a ratio-form guarantee \[ q_0 \;\ge\; \frac{x}{1+x}, \qquad x \;=\; (p{+}1)^2 \sin^2(δ/2)\,C_β, \] where $q_0$ is the single-shot success probability, $C_β$ is the mixer-envelope mass on the optimal set, $δ$ is a phase-gap proxy, and $p$ is the number of layers. Riemann--Lebesgue averaging extends the discussion beyond exact lattice normalization. We conclude by outlining coherent realizations of hardware-efficient positive spectral filters as a main open direction.

翻译：我们研究了约束增强量子近似优化算法（CE-QAOA）的有限层交替，这是一种在块单热流形上原生运行的约束感知参数化量子电路。我们的研究重点在于可行性与最优性保证。我们证明，将代价角限制在调和格点上会揭示作用于代价相位酉算子 $U_C(γ)=e^{-iγH_C}$ 的正费耶滤波器（该分析仅在代价退相参考模型中进行）。在包裹相位分离条件下，这为采样最优解的成功概率提供了与维度无关的有限深度和有限样本下界。具体而言，我们得到了一个比率形式的保证：\[ q_0 \;\ge\; \frac{x}{1+x}, \qquad x \;=\; (p{+}1)^2 \sin^2(δ/2)\,C_β, \] 其中 $q_0$ 是单次采样成功概率，$C_β$ 是混合器包络在最优集上的质量，$δ$ 是相位间隙的代理变量，$p$ 是层数。黎曼-勒贝格平均将讨论扩展到精确格点归一化之外。最后，我们概述了硬件高效正谱滤波器的相干实现作为主要开放研究方向。