What is the name of this quantum gate? As I was watching a video about single qubit quantum gates, I came across the following gate:
$$\begin{bmatrix}e^{i\sigma}&amp;0\\0&amp;e^{i\theta}\end{bmatrix}$$ The video didn't mention the name of the gate. It gave only the matrix and the following information:


$|0\rangle \rightarrow e^{i\sigma}|0\rangle$
$|1\rangle \rightarrow e^{i\theta}|1\rangle$
$\alpha |0\rangle + \beta|1\rangle \rightarrow \alpha e^{i\sigma}|0\rangle + \beta e^{i\theta}|1\rangle$


In the comments below the video, someone asked what $\sigma$ and $\theta$ could be, and the reply was all real numbers, but this was from someone other than the video maker, so I don't know if this is true.

What is the name of this gate?
This is a phase shift gate.

Notice that

$$\begin{bmatrix}e^{i\sigma}&amp;0\\0&amp;e^{i\theta}\end{bmatrix}=
e^{i\sigma}\begin{bmatrix}1&amp;0\\0&amp;e^{i(\theta-\sigma)}\end{bmatrix}
$$

Multiplying the state by a constant (with unit norm) will not affect your measurements.