Pauli Gates
The Pauli gates are fundamental single-qubit operations in quantum computing. They correspond to 180° rotations around the X, Y, and Z axes of the Bloch sphere.
Definitions:
- X gate (bit-flip / NOT):• Action: swaps |0⟩ → |1⟩• Think: 180° rotation around the Bloch sphere's x-axis
- Z gate (phase-flip):• Action: |0⟩ stays |0⟩, |1⟩ → -|1⟩ (adds a π phase to |1⟩)• Think: 180° rotation around the z-axis
- Y gate (bit + phase flip):• Action: |0⟩ → i|1⟩, |1⟩ → -i|0⟩• Think: 180° rotation around the y-axis (like X followed by Z, up to a phase)
Pauli Gates Visualization
Visualization of Pauli-X, Pauli-Y, and Pauli-Z gates on their Bloch sphere axes.
|0⟩
|1⟩
|-⟩
|+⟩
|-i⟩
|i⟩
Pauli-X
|0⟩
|1⟩
|-⟩
|+⟩
|-i⟩
|i⟩
Pauli-Y
|0⟩
|1⟩
|-⟩
|+⟩
|-i⟩
|i⟩
Pauli-Z