Seonggil Lee

Non-Commutative Rough Hybrid Quantum-Classical Information Geometry Dynamics (NC-HQIG): Unifying Hybrid Inseparability, Quantum Fisher Metrics, Noisy Barren Plateaus, and Advantage-Security Duality via UROA, STCT, and RQIG

Realizing practical quantum advantage across the Noisy Intermediate-Scale Quantum (NISQ) and early fault-tolerant regimes requires moving beyond isolated pure-state quantum mechanics to tightly coupled hybrid quantum-classical architectures. This paper establishes Non-Commutative...

Non-Commutative Rough Adaptive Multiscale Dynamics (NC-RAMD): Unifying Category-Theoretic Compositionality, Kan Extensions, Stimulus-Response Lenses, and Adaptive Coalgebras via UROA, STCT, and RQIG

Traditional differential equations and statistical mechanics fail to capture the inter-scale compositionality, bidirectional feedback, and hierarchical adaptivity inherent in complex systems ranging from biological hierarchical materials to port-Hamiltonian physical networks and...