Quantum Hilbert Space: 3D Bloch Sphere
In quantum physics, a qubit's state lives in a 2D complex Hilbert space, spanned by basis states |0⟩ and |1⟩. The Bloch sphere visualizes this state as a vector on a 3D unit sphere, parameterized by angles θ (polar) and φ (azimuthal).
The state is represented as: |ψ⟩ = cos(θ/2)|0⟩ + eiφsin(θ/2)|1⟩.
Dynamic Evolution: The state can evolve under a Hamiltonian (e.g., H = σ_x, causing precession around the x-axis). Here, evolution primarily affects φ.
Interact: Adjust θ and φ with sliders to set the initial state. Click the button to pause/resume time evolution of φ.
Controls
Polar angle: 0 (Up, |0⟩) to π (Down, |1⟩)
Azimuthal angle: 0 to 2π (Rotation around Z-axis)
Current State
|ψ⟩ = cos(0.79)|0⟩ + e^(i0.00)sin(0.79)|1⟩
Initializing 3D Sketch...