Deterministic Reconstruction of HQAP Peaked Circuits via Structural Analysis: An Alternative Explanation to Claimed Quantum Advantage

This work presents a structural analysis of HQAP (Heuristic Quantum Advan-tage Protocol) Peaked Circuits that challenges claimed quantum advantage. We in-troduce Structural Factor Analysis, a methodology that identifies invariant structuralpatterns in quantum circuits to enable deterministic classical reconstruction of hiddenbitstrings. For the HQAP-1917 circuit, our analysis reveals a structural core of 46invariant qubits, reducing the search space from 256 to 210 = 1024 possibilities. Wedemonstrate 100% successful reconstruction of the peak bitstring using classical compu-tation alone, achieving results in minutes that purportedly require quantum hardware.Our findings suggest that structural vulnerabilities in current HQAP constructions un-dermine claims of quantum advantage, and provide a framework for rigorous classicalverification of quantum circuit outputs.