  In the current era of Noisy Intermediate Scale Quantum (NISQ) computing,
efficient digital simulation of quantum systems holds significant importance
for quantum algorithm development, verification and validation. However,
analysis of sparsity within these simulations remains largely unexplored. In
this paper, we present a novel observation regarding the prevalent sparsity
patterns inherent in quantum circuits. We introduce DiaQ, a new sparse matrix
format tailored to exploit this quantum-specific sparsity, thereby enhancing
simulation performance. Our contribution extends to the development of libdiaq,
a numerical library implemented in C++ with OpenMP for multi-core acceleration
and SIMD vectorization, featuring essential mathematical kernels for digital
quantum simulations. Furthermore, we integrate DiaQ with SV-Sim, a state vector
simulator, yielding substantial performance improvements across various quantum
circuits (e.g., ~26.67% for GHZ-28 and ~32.72% for QFT-29 with multi-core
parallelization and SIMD vectorization on Frontier). Evaluations conducted on
benchmarks from SupermarQ and QASMBench demonstrate that DiaQ represents a
significant step towards achieving highly efficient quantum simulations.
