Comparison of Performances for Quantum and Conventional Algorithms: Shor’s algorithm and Boson Sampling

Abstract

Quantum computing has been extensive popularity discussed recently. The foundation of quantum study is the investigation of how quantum computing shows its superiority compared with conventional algorithms. On this basis, this paper focuses on the comparison of the performances of quantum and conventional algorithms about the same relevant area. Two classic problems, factorization of large integer and boson sampling, are chosen to show the specific difference of related quantum and conventional algorithms towards the same problem. This paper specifically compares the performance of Shor's algorithm and other advanced traditional integer factorization algorithms for prime factorization problems and compares the processing capabilities of traditional algorithms and Gaussian Boson sampling for sampling problems. According to the analysis, for the same research problem, quantum algorithms show strong advantages over traditional algorithms in many performances, e.g., time efficiency, algorithm adaptability. It leads to a deeper understanding of quantum superiority and a further explanation of the significance of the development of quantum computing.