Single-Qubit Quantum Gates

Let’s start with some quantum gates that manipulate single-qubit quantum state vectors. The gate shown in the figure below is called a two-qubit gate, with two inputs and two outputs. We will tackle those kinds of gates in Chapter 9. In this chapter, we will focus on how gates manipulate the computational basis states $\ket{0}$ and $\ket{1}$. From there we can figure how they process any other single-qubit state.