Hybrid Quantum-Classical Optimization: A Unified Framework for NISQ Applications

Quantum machine learning (QML) holds transformative potential for solving classically intractable problems, yet its practical implementation on noisy intermediate-scale quantum (NISQ) devices remains hindered by two critical challenges: barren plateaus(exponentially vanishing gradients) and noise-induced gradient corruption. This paper introduces HyQ-OPT, a hybrid quantum-classical optimization framework that systematically addresses these limitations through three innovations: (1) quantum parameter-shift rules for unbiased gradient estimation, (2) noise-adaptive classical momentum to suppress stochastic errors, and (3) dynamic resource allocation based on real-time noise tomography. Theoretical analysis establishes a noise-dependent regret bound of O(T)O(T​) under depolarizing noise (σ≤0.2σ≤0.2), while empirical validation on IBM’s 127-qubit Eagle processor demonstrates 7% accuracy (vs. 86.3% for classical SGD) and a 2.8× speedup in convergence. By maintaining >85% accuracy at σ=0.15σ=0.15, HyQ-OPT outperforms existing methods in both robustness and scalability, paving the way for practical quantum advantage in the NISQ era.