A Lazy Resynthesis Approach for Simultaneous T Gate and Two-Qubit Gate Optimization of Quantum Circuits

State-of-the-art quantum circuit optimization (QCO) algorithms for T-count reduction often lead to a substantial increase in two-qubit gate count (2Q-count) -- a drawback that existing 2Q-count optimization techniques struggle to address effectively. In this work, we propose a novel lazy resynthesis approach for modern tableau-based QCO flows that significantly mitigates the 2Q-gate surges commonly introduced during T-count optimization in Clifford+T circuits. Experimental results show that our approach reduces 2Q-count overhead by 54.8%, 15.3%, and 68.0% compared to tableau-based, ZX-calculus-based, and path-sum-based QCO algorithms, respectively. In terms of runtime, our method achieves speedups of 1.81$\times$ and 13.1$\times$ over the tableau-based and ZX-calculus-based methods, while performing comparably to the path-sum-based approach. In summary, the proposed lazy resynthesis technique not only enhances the quality and performance of tableau-based QCO algorithms but also demonstrates superior efficiency and scalability compared to alternative QCO approaches such as ZX-calculus and path-sum-based techniques.