Quantum simulation plays a critical role in advancing our understanding and development of quantum algorithms, quantum computing hardware, and quantum information science. Despite the availability of various quantum circuit simulators, they often face challenges in terms of maintainability and extensibility. In this paper, we introduce Lightweight Functional Quantum Simulator (LFQS), a compilation-based framework that addresses these issues by leveraging an intermediate language to synthesize efficient quantum simulators in C and CUDA. The intermediate language exploits the underlying structured sparsity behind the matrix representation of quantum gates. Our framework generates efficient code for multi-core CPUs and GPUs and outperforms state-of-the-art simulators, such as Qiskit, Catalyst, and QuEST, as well as a representative of dense tensor frameworks, NumPy, in both micro-benchmark and macro-benchmark circuits.