10
From Circuits to Algorithms

I am among those who think that science has great beauty.

Marie Curie

In the last chapter we became comfortable with putting together gates to create circuits for simple algorithms. We’re now ready to look at more advanced quantum algorithms and considerations on how and when to use them.

Our target in this chapter is Peter Shor’s 1995 algorithm for factoring large integers almost exponentially faster than classical methods. To get there we need more tools, such as phase estimation, the Quantum Fourier Transform, and function period finding. These are important techniques in their own rights, but are necessary in combination for quantum factoring.

We also return to the idea of complexity that we first saw for classical algorithms in section 2.8

This chapter contains more mathematics and equations for quantum computing than we have encountered previously. I recommend that...