A Structural Theory of Quantum Computational Advantage from Admissible Histories

We propose a structural framework for understanding quantum computational advantage based on admissible continuation of configurations. Within this framework, quantum computation is interpreted as the organization of admissible histories whose contributions combine through phase coherence, in a manner related to path-integral formulations of quantum mechanics. We identify three fundamental structural resources: the multiplicity of admissible histories, the persistence of phase coherence, and the non-factorizable structure of continuation constraints (entanglement). We introduce the notion of effective coherent multiplicity as a measure of the portion of history space that contributes constructively to computational outcomes, and formulate a structural speedup conjecture relating superpolynomial quantum advantage to its growth under bounded instability. This perspective provides a unified explanation of both the power and the limitations of quantum computation, clarifying why unstructured problems admit limited speedup while problems with strong global structure can exhibit substantial advantage. The framework complements standard circuit-based complexity theory by relating computational power to the organization of admissible-history space.