Numerical Estimation of Efficiency of the Algorithms Assisting Quantum Factorization

One of the most significant achievements of quantum information processing is the construction of the probabilistic algorithm providing factoring of numbers in polynomial time. However, properties of the classic algorithms assisting an operation of the quantum device have not been well investigated and rough estimates of their effectiveness have been put forth. This paper presents results of the numerical simulation of the quantum factorization algorithm for composite numbers, which have been formed as a product of exactly two factors. It was shown that average factorization efficiency significantly exceeds the commonly used bound. The presented results also provided strong evidence that there exists an internal structure in probability distribution of successful factorization.