  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.
