Pauli-Y Gate | Matrix, Complex Phase & Bit-Phase Flip
Quick Technical Answer:
The Pauli-Y gate performs both a bit-flip and a phase-flip simultaneously with a factor of imaginary unit i: Y|0⟩ = i|1⟩ and Y|1⟩ = -i|0⟩. It represents a 180° rotation around the Y-axis of the Bloch sphere.
Formula / Unitary:
Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} = iXZ
Simulate this in Itachi Quantum Studio
Inspect state amplitudes, 3D Bloch sphere vector, and OpenQASM code live.
Algebraic Properties
The Pauli-Y operator anti-commutes with X and Z ({X, Y} = {Y, Z} = 0) and satisfies the commutation relation [X, Y] = 2iZ. Its eigenstates on the Bloch sphere equator are |+i⟩ = (|0⟩ + i|1⟩)/√2 and |-i⟩ = (|0⟩ - i|1⟩)/√2.
Frequently Asked Questions
What is the relationship between Pauli-X, Y, and Z gates?
The Pauli matrices satisfy Y = iXZ. Pauli-Y combines the bit-flip action of X with the phase-flip action of Z and a global phase of i.