The rapid advancement of quantum computing has led to the development of various quantum libraries, empowering compilation, simulation, and hardware backend interfaces. However, ensuring the correctness of these libraries remains a fundamental challenge due to the lack of mature testing methodologies. The state-of-the-art tools often rely on domain-specific configurations and expert knowledge, which limits their accessibility and scalability in practice. Furthermore, although these tools demonstrate strong performance, they adopt measurement-based for output validation in testing, which makes them produce false positive reports. To alleviate these limitations, we propose QSPE, a practical approach that follows the differential testing principle and extends the existing approach, SPE, for quantum libraries. QSPE is fully automated, requiring no pre-set configurations or domain expertise, and can effectively generate a large set of diverse program variants that comprehensively explore the quantum compilation space. To mitigate the possible false positive reports, we propose statevector-based validation as an alternative to measurement-based validation. In our experiments, the QSPE approach demonstrates remarkable effectiveness in generating 22,770 program variants across multiple quantum computing platforms. By avoiding $α$-equivalence at the quantum and classical program wise, QSPE can reduce redundant generation and save more than 90\% of execution cost. Finally, the statevector-based validation method assists QSPE to reduce false alarms and effectively detects 708 miscompilations across multiple quantum libraries. Notably, 81 of the discovered bugs have been officially approved and acknowledged by the Qiskit development team, demonstrating the practical impact of our approach.