Improving the performance of quantum adder is an important technical challenge with major impact on the implementation of efficient, large-scale quantum computing. Continuing along this research direction, we propose a novel parallel-prefix quantum adder based on Ling expansion. We systematically explored classical structures for parallel-prefix adders assessing their suitability to be realized in quantum domain. Furthermore, Ling adder enforces Logical OR and large fan-out, which require innovative solutions. We addressed these challenges to realize the quantum Ling adder, which results in a T-depth of only $O\left( {\log \frac{n}{2}} \right)$. This represents a substantial improvement over the previous quantum adders based on parallel prefix structure, which require O(log n) T-depth. We present extensive theoretical and simulation-based studies to establish our claims.