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The quantum approximate optimization algorithm (QAOA) has become acornerstone of contemporary quantum applications development. Here we show thatthe \emph{density} of problem constraints versus problem variables acts as aperformance indicator. Density is found to correlate strongly withapproximation inefficiency for fixed depth QAOA applied to random graphminimization problem instances. Further, the required depth for accurate QAOAsolution to graph problem instances scales critically with density. Motivatedby Google's recent experimental realization of QAOA, we preform a reanalysis ofthe reported data reproduced in an ideal noiseless setting. We found that thereported capabilities of instances addressed experimentally by Google, approacha rapid fall-off region in approximation quality experienced beyondintermediate-density. Our findings offer new insight into performance analysisof contemporary quantum optimization algorithms and contradict recentspeculation regarding low-depth QAOA performance benefits.

Reachability Deficits in Quantum Approximate Optimization of Graph Problems