Reducing T-Depth and T-Count in Quantum Multiplication Using Compressor Primitives

Optimization of quantum multiplication is a critical area of study due to its pivotal role in quantum algorithms such as Shor’s factorization. Every time a quantum multiplier is used, it repeatedly executes several key components to perform the multiplication. Most current works have focused on using components such as the basic half and full-adder designs, which have limited efficiency. In this paper, we demonstrate that by using a generalized (m:k) compressor-based Wallace Tree one can significantly improve efficiency; this method achieves reductions of up to 92.8% in T-Depth and 55.6% in T-Count while maintaining a competitive Qubit-Count through brute-force and dynamic programming optimization.