Lecture 12. Period finding and number factorization

In this Lecture we discussed how quantum circuits are used to solve the problem of finding the period of a integer argument function. For its solution we use a technique similar to Simon's algorithm and properties of chained fractions. This algorithm allows to solve the hidden subgroup problem in any finitely generated abelian group, including the problem of finding the order of one number modulo another. Thanks to this, one can efficiently find nontrivial divisors of large numbers.