9. Gates: Pauli Matrices

Pauli Matrices (X, Y, Z)

The single-qubit gates are rotations. The most fundamental ones are the Pauli matrices:

• X (Bit Flip): Swaps $|0\rangle$ and $|1\rangle$. (Rotation around X-axis)
• Y (Bit & Phase Flip): Swaps $|0\rangle$ and $|1\rangle$ and adds a phase. (Rotation around Y-axis)
• Z (Phase Flip): Leaves $|0\rangle$ alone but flips the sign of $|1\rangle$. (Rotation around Z-axis)