The RQPE circuit generation algorithm can be further optimized by exploring different reduction strategies that can efficiently handle a larger set of phases while minimizing the number of qubits and unitary applications required. One approach could involve refining the algorithm to identify patterns in the phase sets that allow for more efficient reductions. By optimizing the sequence of operations in the algorithm, such as the selection of GCDs and additions, it may be possible to streamline the process and reduce the overall complexity. Additionally, incorporating advanced mathematical techniques or algorithms, such as dynamic programming or heuristic methods, could help in finding more optimal solutions for generating RQPE circuits. Furthermore, leveraging machine learning algorithms to analyze and predict the most effective reduction steps based on the input phase set could lead to further improvements in the algorithm's performance.