Finite-Depth, Finite-Shot Guarantees for Constrained Quantum Optimization via Fejér Filtering

• URL: http://arxiv.org/abs/2603.01809v1
• Date: Mon, 02 Mar 2026 12:44:19 GMT
• Title: Finite-Depth, Finite-Shot Guarantees for Constrained Quantum Optimization via Fejér Filtering
• Authors: Chinonso Onah, Kristel Michielsen,
• Abstract summary: We show that restricting cost angles to a harmonic lattice exposes a positive Fejér filter acting on the cost-phase unitary $U_C()=e-iH_C$ emphin a cost-dephased reference model.<n>Under a wrapped phase-separation condition, this yields emphdimension-free finite-depth and finite-shot lower bounds on the success probability of sampling an optimal solution.
• Score: 0.2578242050187029
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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