Shor's Quantum Factorization Algorithm (part 1 of 2)

We'll do a pedagogical review of Shor's factorization algorithm -- a quantum algorithm for factoring large numbers into its prime factors. This paper has over 16k citations (!!!), and is an indisputable classic in the field of quantum computing. You can find the paper on the Arxiv here: https://arxiv.org/abs/quant-ph/9508027

My background is in theoretical physics, and I've taken a course in quantum computing (many years ago). I'll try to give a gentle introduction to this topic, and will cover some preliminaries of quantum computing. Please try to read the paper beforehand even if you have no background in quantum mechanics -- it does contain some preliminaries that might give you a solid starting place.

In this first meeting, I'll cover the classical factorization algorithm. This will be necessary background before we can understand a quantum version of that algorithm. Depending on timing, we may go into some of the preliminaries for quantum computing (understanding qubits and quantum gates) this meeting, or may save that for next time. Alternatively, if each meeting goes long, this may turn into a 3-part series.