What is the Pauli-Z gate?

What is the Pauli-Z gate?

The Pauli-Z gate is a fundamental gate in quantum computing that operates on a single qubit. It is represented by the matrix:

[[1, 0],
[0, -1]]

When applied to a qubit in the computational basis, the Pauli-Z gate flips the sign of the qubit's state |1⟩, while leaving the state |0⟩ unchanged. In other words, it applies a phase shift of π radians to the |1⟩ state.