A numerical simulation of quantum factorization success probability

Abstract

The quantum factorization is probably the most famous algorithm in quantum computation. The algorithm succeeds only when some random number with an even order relative to factorized composite integer is fed as the input to the quantum order finding algorithm. Moreover, post processing of the quantum measurement recovers the correct order only for some subset of possible values. It is well known that numbers with even orders are found with probability not less than 1/2. However, numerical simulation proves that probability of such event exhibits grouping on some discrete levels above that limit. Thus, one may conclude that usage of the lowest estimate leads to underestimation of the successful factorization probability. The understanding of the observed grouping requires further research in that field.