Circuit QED › Interactive › Bloch Sphere
3D InteractiveSingle-qubit gates
Bloch Sphere
Every pure single-qubit state lives on the surface of the Bloch sphere. Apply gates to rotate the state vector and watch the geometry of quantum operations.
Apply gate
Prepare state
Decoherence — conceptual reference
Select a decay channel to see how decoherence constrains the Bloch vector. T₁ drives the state toward |1⟩ (energy relaxation); T₂ dephases the equatorial components without changing the z-component.
Gate reference
Xπ rotation around X
Yπ rotation around Y
Zπ rotation around Z
HHadamard — |0⟩ → |+⟩
Sπ/2 phase gate
Tπ/4 phase gate
S†S dagger (–π/2 phase)
T†T dagger (–π/4 phase)