Gates as Matrices

We saw in the previous chapter that computation can be carried out by using logic gates to act on the Cbits carried by the wires in the computer’s electrical circuits. We described the results of those operations using logic tables (or truth tables).

There is another neat way of representing what gates do to classical computing bits. To illustrate this, let’s consider the $\text{NOT}$ gate. Remember that a $\text{NOT}$ gate changes a bit $0$ into a bit $1$ and a bit $1$ into a bit $0$. How would we write those results in state vector language?