Quantum-Classical Advantage Boundaries: An Analytical Framework for Hybrid QPU-GPU
approvedThe emergence of hybrid quantum-classical architectures integrating quantum processing units (QPUs) with GPU-accelerated classical co-processors has outpaced the development of formal frameworks for predicting when such systems achieve computational advantage. We introduce the \emph{Quantum-Classical Advantage Boundary} (QCAB) framework, a parameterized analytical model that delineates the regimes in which hybrid QPU-GPU computation surpasses purely classical methods for quantum simulation tasks. The framework defines a \emph{Quantum Utility Ratio} $\QUR(n, d, S, \tau, \varepsilon)$ over the five-dimensional parameter space of qubit count $n$, circuit depth $d$, entanglement entropy $S$, communication latency $\tau$, and hardware error rate $\varepsilon$. We derive closed-form expressions for the advantage boundary surface under both state-vector and tensor-network classical baselines, and establish scaling laws governing the transition from classical to quantum computational dominance.
