An Archetypal Taxonomy of Quantum Logic Gates: A Semantic Framework for Explainable Quantum Computing

The quantum computing industry faces a persistent explanatory gap: the mathematical formalism of quantum logic gates is precise and powerful, yet remains largely inaccessible to the broader scientific and engineering communities. This work introduces a structured semantic framework that applies seven archetypal dimensions—Matrix, Potentiator, Catalyst, Experience, Significator, Transformation, and Way—as a descriptive interpretive layer to a comprehensive taxonomy of 50 quantum logic entities. This master taxonomy is comprised of 36 individual quantum logic gates organized across 6 operational classes and 6 subgroups, anchored by 2 foundational entities. The Seven Prime Archetypes function not as redefinitions of quantum mechanical concepts, but as a rigorous, philosophically coherent translation of quantum operations into human-interpretable language. Each archetype illuminates a distinct dimension of a gate's operational identity: its foundational substrate (Matrix), latent potential (Potentiator), mechanism of action (Catalyst), observable signature (Experience), formal mathematical representation (Significator), transformational character (Transformation), and governing operational principle (Way). This taxonomy establishes a functional "Periodic Table" of quantum logic, bridging the gap between abstract unitary mathematics and semantic meaning. Furthermore, this framework serves as the foundational logic for Explainable Digital Intelligence (XDI), demonstrating how structural interpretability can be embedded into quantum neural architectures at genesis rather than extracted post-hoc. By formalizing the semantic geometry of quantum gates, this work provides researchers, educators, and algorithm designers with a novel conceptual toolkit for contextualizing the operational complexity of quantum computation.