Fidelity Thresholds for QAOA Depth Benefits: A Noise-Scaled Simulation Study for Fault Tree QUBO Instances

This paper presents a noise-scaled simulation study to characterize whether increased QAOA circuit depth provides measurable improvement for fault tree QUBO instances under varying two-qubit gate fidelity conditions. Using 60 fault tree instances with circuits loaded via QPY serialization, we executed 960 simulations spanning depths p = 1 and p = 2 across a fidelity sweep from F₂ = 0.900 to F₂ = 0.992, with fixed single-qubit fidelity F₁ = 0.9995 and readout fidelity Fro = 0.97. The primary finding is that output distributions are noise-dominated and shot-limited at all tested fidelity levels. Maximum probability values cluster near the shot floor of 1/1024, and Shannon entropy approaches the measurement ceiling of 10 bits. The median difference between depth p = 2 and depth p = 1 is exactly zero for maximum probability at all fidelity levels. No consistent improvement in distribution concentration is observed as fidelity increases within the tested range. These results establish that no depth benefit is detectable through F₂ = 0.992 under this noise model and shot budget. Practitioners should not expect depth scaling to improve output quality until gate fidelity exceeds the upper bound of this sweep. This completes the investigation arc from prior work: depth does not help on current hardware because noise accumulation exceeds algorithmic signal, and this finding persists through the tested fidelity range.