Abstract

The advent of Noisy Intermediate-Scale Quantum (NISQ) devices presents unprecedented opportunities for practical quantum computing applications, yet optimization challenges remain significant barriers to achieving quantum advantage. This study investigates the optimization of Variational Quantum Eigensolvers (VQEs) for ground state energy estimation in molecular systems using hybrid classical-quantum architectures. We implemented and evaluated novel parameter initialization strategies and adaptive optimization protocols across three NISQ simulators and one hardware platform. Our methodology employed a 16-qubit quantum circuit with parameterized gates, testing on hydrogen chains of varying lengths (H2, H4, H6, H8). Results demonstrate that our adaptive gradient-descent approach achieves 94.3% accuracy in ground state energy estimation for H2 molecules, with a 67% reduction in circuit depth compared to standard approaches. Statistical analysis reveals significant improvements in convergence rates (p < 0.001) and mitigation of barren plateau phenomena. The hybrid architecture successfully maintained coherence times sufficient for practical implementation, demonstrating clear pathways toward fault-tolerant quantum computing applications. These findings contribute to advancing quantum computational chemistry and establish benchmarks for future NISQ-era quantum algorithms.