Feasibility-aware warm-initialized QAOA for constrained cloud–fog task scheduling under NISQ-oriented noise

Constrained task scheduling in cloud–fog environments is challenging because heterogeneous resources, latency and energy requirements, and capacity constraints create a combinatorial optimization problem in which QAOA may generate infeasible schedules. This paper proposes a feasibility-aware hybrid quantum–classical framework combining Warm-Initialized QAOA with constraint-aware decoding and joint CP-SAT repair under noisy intermediate-scale quantum (NISQ)-oriented conditions. The scheduling problem is formulated as a quadratic unconstrained binary optimization (QUBO) model that jointly captures latency–energy optimization, deadlines, and resource capacities. The framework is evaluated on 12 structured benchmark instances spanning balanced, capacity-tight, deadline-tight, and heterogeneous regimes, with executable QUBOs containing 20–22 logical qubits. Across 96 production configurations under ideal, low, medium, and high noise conditions, 91 configurations ( $$94.79\%$$ ) produced at least one schedule-feasible sampled candidate before repair; this configuration-level success rate is distinct from the shot-level schedule-feasible probability. The joint CP-SAT repair stage successfully restored feasibility in all five configurations for which no feasible sampled candidate was available, yielding $$100\%$$ post-repair feasibility and reducing the mean constraint-violation count from $$0.09375$$ to $$0$$ . For the 91 configurations with a feasible pre-repair selected candidate, the paired mean optimality gap remained unchanged at $$10.60\%$$ after repair, whereas the post-repair mean over all 96 configurations was $$10.79\%$$ because the five repaired cases entered the post-repair denominator. Matched attribution controls further show that the schedule-feasible probability increases from $$0.44\%$$ for uniform initialization at $$p=0$$ to $$29.86\%$$ for warm initialization at $$p=0$$ and $$30.52\%$$ for Warm-Initialized QAOA at $$p=1$$ , indicating that the dominant feasible-region concentration arises from warm initialization, with a smaller incremental contribution from the shallow QAOA evolution. Additional sensitivity, classical-reference, and GPU scalability experiments characterize parameter dependence, classical competitiveness, runtime, and sampling behavior within the investigated NISQ-oriented simulation regime.