Gates & Circuits
Pauli Gates (X, Y, Z)
A set of three fundamental single-qubit gates — X (bit flip), Y, and Z (phase flip) — named after physicist Wolfgang Pauli.
Definition
The Pauli gates are three of the most basic single-qubit quantum gates. The X gate acts like a classical NOT gate, flipping |0⟩ and |1⟩. The Z gate flips the sign of the |1⟩ amplitude without changing measurement probabilities directly. The Y gate combines aspects of both.
Technical Definition
Represented as 2×2 matrices, X = [[0,1],[1,0]], Z = [[1,0],[0,-1]], and Y = [[0,-i],[i,0]]. Together with the identity matrix, these four matrices form a basis that can describe any single-qubit operation and are foundational to describing quantum error types (bit-flip and phase-flip errors).
Visual Explanation: An Analogy
Think of the X gate like flipping a coin from heads to tails, while the Z gate is more subtle — like marking the 'tails' side with an invisible minus sign that doesn't change what you see when you look at the coin, but does change how it interacts in further calculations.
Real-World Use Cases
- X gates and Z gates describe the two fundamental error types in quantum error correction (bit-flip and phase-flip errors)
- Used throughout quantum circuit constructions as basic building blocks
- The Mini Quantum Circuit Builder tool on this site lets you experiment with X and Z gates directly