Quantum Gate
Just like a logic gate that acts on bits, a quantum gate acts on qubits, transforming them from one state to another. It is often denoted by the capital letter $U$. 1
A quantum gate must be linear, i.e. we can distribute it across superpositions: $$U(\alpha \ket 0 + \beta \ket 1) = \alpha U \ket 0 + \beta U \ket 1.$$
Quantum gates are linear maps that keep the total probability equal to 1. They are a type of matrix called Unitary matrix, which is why the are often labeled as $U$.