This is the first in a series of blog posts exploring the compilation of quantum algorithms to fault-tolerant architectures. We will

1. begin with the classical Hamming code,
2. extend it to the quantum Steane code,
3. learn about compilations of $T$-gates via magic state distillation,
4. reproduce key papers describing fault-tolerant compilation, and
5. explore methods to optimize the implementation of quantum simulation algorithms on early fault-tolerant devices

The series will focus on specifics (specific code, specific decoder, specific algorithm), and will aim to build intuition through numerical experiments. In this post, I will give an overview of the $[[7,4,3]]$ Hamming code.