Chapter 3 Quantum gates

About understanding the square root of \texttt{NOT} via a physical implementation using symmetric beam-splitters. More about the Bloch sphere, via the omnipresent Pauli matrices, which can be described in a more algebraic way.

Before moving on, we first study two of the subjects from Chapter 2 in more depth: the square root of \texttt{NOT}, and the Bloch sphere.

The goal for the latter is to be able to visualise sequences of unitary operations on a qubit as sequences of rotations, and to see the action of some quantum circuits without getting engaged in lengthy calculations. The goal for the former is to study a way of implementing this gate using physical experiments, and then studying a related construction (the so-called Mach–Zehnder interferometer).