State the Pauli matrices and apply Pauli matrices on the states |0⟩ and |1⟩.

Basis States:

We represent the standard quantum states as column vectors:

Applying Pauli Matrices on ∣0⟩and ∣1⟩:

Pauli-X

It flips the bit — just like NOT gate.

Pauli-Y

It flips the bit and adds a phase shift.

Pauli-Z

It leaves |0⟩ unchanged and adds a phase flip to ∣1⟩|1⟩∣1⟩.