Abstract
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 Fej\'er filter acting on the cost-phase unitary U_C(γ)=e^-iγ H_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 q₀ ≥ x/1+x, x = (p+1)² sin²(δ/2)C_β, where q₀ 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. A Coherent equivalent is proved subsequently and a Riemann--Lebesgue averaging extends the discussion beyond exact lattice normalization. We conclude by outlining coherent realizations of near-term-hardware-efficient positive spectral filters as a main open direction for this framework.