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--- x-gate [May 25, 2026 at 10:17] – Ivan Janevski
+++ x-gate [May 25, 2026 at 10:21] (current) – Ivan Janevski
@@ Line 1: / Line 1: @@
 # X-gate
-**X-gate** (or **Pauli-X gate** / **Quantum NOT gate**) is a quantum gate that serves as the quantum equivalent of logical NOT. Applying X to the qubit $\lvert 0\rangle$ yields $\lvert 1\rangle$, and applying X to the qubit $\lvert 1\rangle$ yields $\lvert 0\rangle$.
+**X-gate** (or **Pauli-X gate** / **Quantum NOT gate**) is a 1-qubit quantum gate that serves as the quantum equivalent of logical NOT. It's represented by the following 2x2 matrix.
-$$X = \begin{pmatrix}0 & 1\\1 & 0\end{pmatrix}$$
+$$ X = \begin{pmatrix}0 & 1\\ 1 & 0\end{pmatrix}$$
+The gate flips $\lvert 0\rangle$ to $\lvert 1\rangle$, and $\lvert 1\rangle$ to $\lvert 0\rangle$, which is why it's called the quantum equivalent of NOT.
+On the Bloch sphere, it rotates the state by $\pi$ radians (180 degrees) around the X-axis.