Not yet reviewed by Pith; the record is open.

Quantum computing enables parallelism through superposition and entanglement and offers advantages over classical computing architectures. However, due to the limitations of current quantum hardware in the noisy intermediate-scale quantum (NISQ) era, classical simulation remains a critical tool for developing quantum algorithms. In this research, we present a comprehensive parallelization solution for the Q$^2$Chemistry software package, delivering significant performance improvements for the full-amplitude simulator on both CPU and GPU platforms. By incorporating batch-buffered overlap processing, dependency-aware gate contraction and staggered multi-gate parallelism, our optimizations significantly enhance the simulation speed compared to unoptimized baselines, demonstrating the effectiveness of hybrid-level parallelism in HPC systems. Benchmark results show that Q$^2$Chemistry consistently outperforms current state-of-the-art open-source simulators across various circuit types. These benchmarks highlight the capability of Q$^2$Chemistry to effectively handle large-scale quantum simulations with high efficiency and high portability.