Noise-Aware Quantum Approximate Optimization for Carbon-Aware Scheduling of Renewable Generation, Battery Storage and Industrial Loads

Carbon-aware scheduling of flexible plant assets couples a price signal and a time-varying grid carbon intensity to the dispatch of battery storage and deferrable industrial loads, which turns an otherwise small unit-scheduling task into a constrained binary program whose landscape is dominated by penalty terms. This paper examines whether the Quantum Approximate Optimization Algorithm (QAOA) can be made a credible solver for that program on noisy devices, with the negative findings reported alongside the positive ones. A multiobjective quadratic unconstrained binary optimization (QUBO) model is derived in which energy cost, a carbon price applied to the grid carbon intensity, a quadratic peak-demand surrogate and an end-of-horizon valuation of stored energy share one quadratic form; terminal battery neutrality is imposed in cycle-count space so that round-trip losses do not distort the constraint, and a state-of-charge excursion regularizer is shown to have a usable weight window within which the penalized optimum is feasible and within 0.08 % of the constrained optimum. Price and carbon signals are derived from hourly economic dispatch of the IEEE 14-bus generators, which exposes a marginal emission factor that is almost flat under coal-first merit order; the average emission factor is therefore used as the primary signal and the difference is quantified. For noise, a closed-form proposition shows that global depolarizing noise contracts the QAOA energy without moving its optimizers, which converts depth selection into a one-line rule validated numerically; for local depolarizing noise, re-optimization on a common-random-number trajectory surrogate recovers at most 0.029 in normalized gain over transferred angles once optimizer convergence is controlled for. On 12-, 15- and 18-qubit instances, QAOA at depth six concentrates between 34 % and 68 % of its probability on the feasible subspace and a feasibility-filtered decoder with 1000 shots reaches the constrained optimum to within 0.15 %; simulated annealing with the same sample budget reaches it exactly. The results support QAOA as a structured sampler for this problem class while placing its present advantage, if any, outside the regime reachable by exact simulation.