Chapter 1
Foundations of Quantum Computing

The beginning is always today.
— Mary Shelley

You may have heard that the mathematics needed to understand quantum computing is arcane, mysterious and difficult…but we utterly disagree! In fact, in this chapter, we will introduce all the concepts that you will need in order to follow the quantum algorithms that we will be studying in the rest of the book. Actually, you may be surprised to see that we will only rely on some linear algebra and a bit of (extremely simple) trigonometry.

We shall start by giving a quick overview of what quantum computing is, what the current state of the art is, and what the main applications are expected to be. After that, we will introduce the model of quantum circuits. There are several computational models for quantum computing, but this is the most popular one and, moreover, it's the one that we will be using throughout most of the book. Then, we will describe in detail what qubits are, how...