Quantum Walks on Configuration Matroids: A Rigorous Framework for Electrical Network Reconfiguration with Provable Speedup

This document is a research preprint and technical manuscript presenting QWCM (Quantum Walk on Configuration Matroid), a structured quantum algorithm for electrical distribution network reconfiguration based on matroid theory and quantum walks. The work develops a rigorous theoretical framework exploiting the graphic matroid structure of radial network configurations and recent results on strong log-concavity of matroids, leading to provable spectral gap guarantees and quadratic quantum speedup in hitting time under the standard oracle model. The manuscript clearly distinguishes between proven theoretical results, oracle-level complexity analysis, and numerical validation through classical simulation on standard IEEE test networks. A hybrid quantum–classical architecture is proposed to avoid known conditioning barriers of direct quantum linear system approaches. Status: Draft for review. This version is intended to establish priority and enable academic discussion. The manuscript may be revised prior to submission to a peer-reviewed venue.