Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be “translated” to a series of simple steps, each of which the computer knows how to do. This task is relatively easy to do on a classical computer and we witness the benefits of this success in our everyday life. Quantum mechanics, the physical theory of the very small, promises to enable completely novel architectures of our machines, which will provide specific tasks with higher comput- ing power. Translating and implementing algorithms on quantum computers is hard. However, we will show that solutions to this problem can be found and yield surprising applications to number theory.