Pauli-Z Gate (Phase-Flip) | Matrix, Telemetry & Eigenstates
Quick Technical Answer:
The Pauli-Z gate leaves the computational state |0⟩ unchanged while shifting the phase of state |1⟩ by π radians: Z|0⟩ = |0⟩ and Z|1⟩ = -|1⟩. It executes a 180° rotation around the Z-axis of the Bloch sphere.
Formula / Unitary:
Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, \quad Z|0\rangle = |0\rangle, \quad Z|1\rangle = -|1\rangle
Simulate this in Itachi Quantum Studio
Inspect state amplitudes, 3D Bloch sphere vector, and OpenQASM code live.
Phase Flip in Quantum Computation
The Pauli-Z gate acts as a phase-reversal operator. It leaves measurement probabilities in the computational basis completely unchanged (|α|² and |β|² remain constant) but inverts the relative phase between basis states.
Frequently Asked Questions
Does the Pauli-Z gate change measurement probabilities?
No. When measured in the computational Z-basis, the measurement probabilities for |0⟩ and |1⟩ are unaffected by a Z gate. However, in the X-basis (|+⟩ and |-⟩), applying Z swaps the states.