Pauli-X / NOT¶
The Pauli-X gate, shown in Qompile's catalog as NOT, is the quantum equivalent of a classical NOT gate - it flips \( |0\rangle \) to \( |1\rangle \) and vice versa.
| Qubits | 1 |
| Parameters | None |
| Inverse | Itself (X² = I) |
| Also called | X gate, bit-flip gate, quantum NOT |
What it does¶
X swaps the amplitudes of \( |0\rangle \) and \( |1\rangle \). Applied to a definite state it behaves exactly like a classical bit flip; applied to a superposition it swaps the two amplitudes while leaving their values (and any phase) otherwise intact.
Matrix¶
Action on basis states¶
- \( |0\rangle \rightarrow |1\rangle \)
- \( |1\rangle \rightarrow |0\rangle \)
Phase and Bloch-sphere effect¶
On the Bloch sphere, X is a 180° rotation about the X-axis. It swaps the north and south poles (\( |0\rangle \) and \( |1\rangle \)) and leaves points on the X-axis unmoved.
Example¶
Placing X on q[0] (initially \( |0\rangle \)) prepares \( |1\rangle \) - the Probabilities panel then shows 100% on outcome 1.
Other notations¶
Naming conventions across ecosystems; exact syntax can vary by library version, and this does not claim to be Qompile's generated output unless otherwise noted.
| Language | Typical form |
|---|---|
| OpenQASM 2.0 | x q[0]; |
| Qiskit | circuit.x[q[0]] |
| Cirq | cirq.X(q[0]) |
| Q# | X(q[0]); |