QuantumPhaseNet: A Gauge-Covariant Geometric and Quantum-Spectral Theory of Semantic Concept Hierarchies with Prototype Validation of a Classical Quantum-Inspired Model

Abstract

We present QuantumPhaseNet, a gauge-covariant geometric and quantum-spectral extension of Transformer representations. Context-dependent semantic states are modeled as complex amplitudes; a covariant phase rate induces a semantic wavelength used as a proxy for conceptual scale; and low-frequency graph modes define a document-level discourse direction. The theoretical part establishes local gauge invariance, unitarity of the quantum block, boundedness and conditional stability of WavePhase Attention, and a calibratable hallucination-risk formulation. We also implemented a fully offline Validation Studio for the classical quantum-inspired pipeline in Section 14.1 and evaluated the five research questions in Section 16.1 on its built-in synthetic setting (n=240, observation noise 0.22, circuit noise 0.08, five seeds). RQ1 yielded a wavelength-hierarchy Spearman correlation of 0.852 versus 0.707 for the baseline, 87.3% direction accuracy, and AUC 0.953. RQ2 achieved discourse alignment 0.933 versus 0.589 and 41.2 versus 16.2 paragraphs before drift. RQ3 achieved AUROC 0.881 versus cosine 0.765 and phase-shuffle 0.536. RQ4 achieved error-detection AUROC 0.854 versus entropy 0.634, with Brier 0.150 and ECE 0.098. RQ5 did not show quantum advantage: target probability and end-to-end cost efficiency were 25.5% and 0.107, compared with 70.7% and 0.707 for the Chebyshev classical approximation. These results provide initial synthetic evidence for the classical quantum-inspired components, but not external validity or unconditional quantum speedup.