No Quantum Advantage for Closed-Loop Cognitive Systems (NQA-CLCS)

Abstract This paper establishes a formal negative result: for a broad and practically relevant class of closed-loop cognitive systems, quantum computation provides no fundamental advantage over classical architectures. We show that when system performance is governed by recursive closure, event-driven contraction, and forward-invariant trust manifolds, achievable robustness, memory persistence, and adaptive stability are determined by architectural dynamics rather than computational substrate. We formalize this result via a hybrid automaton model, derive explicit trust-floor bounds, construct a Lyapunov functional proving invariance under bounded perturbations, and demonstrate thermodynamic dominance of closure-based systems. A hybrid Sentinel–lattice corollary shows how exploratory dynamics may be safely embedded without sacrificing invariance. The results imply that for cognition, security, and adaptive control workloads, quantum computers are architecturally redundant.