Bloch Sphere

The Bloch sphere provides a powerful visual representation of how single-qubit gates transform quantum states. Each gate corresponds to a geometric rotation or reflection of the state vector on the sphere.

Bloch Sphere
A geometric representation of qubit states in three-dimensional space.
|ψ⟩
Z
|0⟩
|1⟩
X
|-⟩
|+⟩
Y
|-i⟩
|i⟩

Axis Descriptions:

Z-Axis (Vertical)

North pole: |0⟩ state
South pole: |1⟩ state

X-Axis (Horizontal)

Right: |+⟩ = (|0⟩ + |1⟩)/√2
Left: |-⟩ = (|0⟩ - |1⟩)/√2

Y-Axis (Into/Out of page)

Forward: |i⟩ = (|0⟩ + i|1⟩)/√2
Backward: |-i⟩ = (|0⟩ - i|1⟩)/√2

About Felix Bloch

The Bloch sphere is named after physicist Felix Bloch, who made significant contributions to nuclear magnetic resonance and quantum mechanics.