Computing Library › Quantum Logic Gates
Quantum Logic Gates
Pauli-X Gate (NOT)
The Pauli-X gate is the quantum NOT — it flips |0⟩ and |1⟩ and rotates the Bloch vector 180° about the x-axis.
Matrix
Unitary matrix
0110
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |0⟩ | |1⟩ |
| |1⟩ | |0⟩ |
| |+⟩ | |+⟩ |
| |−⟩ | −|−⟩ |
How it works
X is the bit-flip. On the Bloch sphere it is a π rotation about x. It is Hermitian (X=X†) and its own inverse (X²=I), and it is a member of the Clifford group. Together with Z it generates the bit/phase structure every error-correction code tracks.
In code (Qiskit)
python
qc = QuantumCircuit(1)
qc.x(0) # |0> -> |1>single-qubitPauliCliffordHermitian