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In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
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Difference between operators used to represent quantum gates vs that to represent physical o...
But as I am learning quantum gates now, I see that even the gates are represented by operators (or matrices). But they do change the state of the quantum system. …