Efficient Depth Optimization in Quantum Addition and Modular Arithmetic with Ling Structure

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 \(O(\log \frac{n}{2})\) . This represents a substantial improvement over the previous quantum adders based on parallel prefix structure, which require \(O(\log n)\) T-depth. Based on the proposed adder, an efficient quantum modular adder is also demonstrated in this paper, further extending the applicability of our approach. We present extensive theoretical and simulation-based studies to establish our claims.