Abstract
<title>Abstract</title> <p>We benchmark classical, simulated-quantum, hybrid, and direct quantum-annealing workflows on a structured binary control problem formulated as a quadratic unconstrained binary optimization (QUBO) model. The benchmark is motivated by greenhouse heater scheduling, where the horizon \((H)\) denotes the number of hourly binary control decisions, but the focus is on solver behavior for a physically decoded control-QUBO formulation. For the main one-day instance (\((H=24)\)), all solver outputs are decoded back into heater schedules and evaluated using the same simulator-side objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid binary quadratic model workflow is less reliable and does not outperform the classical baselines under 15--60 s requested time limits. Direct D-Wave quantum processing unit execution on reduced instances remains feasible in all runs and recovers the exact optimum for \((H=10)\) and \((H=12)\), but the exact-hit rate decreases with increasing horizon. The results do not indicate quantum advantage, but provide a reproducible benchmark for evaluating annealing-based natural and quantum computing workflows on structured control QUBOs. MSC Classification: 90C27 , 90C59 , 81P68 , 93C55</p>