With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum algorithms is crucial, as it can provide insights into the practical feasibility from the current perspective. In this chapter, we aim to analyze the time required for integer factorization tasks using Shor's algorithm within a gate-based quantum circuit simulator of the matrix product state type. Additionally, we observe the impact of parameter pre-selection in Shor's algorithm. Specifically, this pre-selection is expected to increase the success rate of integer factorization by reducing the number of iterations and facilitating performance measurement under fixed conditions, thus enabling scalable performance evaluation even on real quantum hardware.

翻译：随着量子技术的发展，基于整数分解的传统加密系统面临潜在威胁。因此，开发精确测量相关量子算法性能的技术至关重要，这有助于从当前视角洞悉其实际可行性。本章旨在分析基于矩阵乘积态型门级量子电路模拟器中使用肖尔算法执行整数分解任务所需的时间。此外，我们观察到肖尔算法中参数预选的影响。具体而言，这种预选可通过减少迭代次数来提升整数分解的成功率，并在固定条件下便于性能测量，从而即使在真实量子硬件上也能实现可扩展的性能评估。