⚛️ Bloch Sphere Simulator
Module 2
3D Single-Qubit Parameterization: Polar Angle θ & Azimuthal Phase ϕ
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Section 1 Basis Presets
|0⟩
North (+z)
|1⟩
South (−z)
|+⟩
+x (Real)
|−⟩
−x (Real)
|+i⟩
+y (Imag)
|−i⟩
−y (Imag)
Polar Angle
θ
(Colatitude)
58.0° (0.32π)
Azimuthal Phase
ϕ
(Equator)
54.0° (0.30π)
▶
Auto-Sweep Relative Phase ϕ
Measurement Probabilities
P(0) = cos²(θ/2)
76.5%
P(1) = sin²(θ/2)
23.5%
Quantum State Representation
|ψ⟩ = 0.875 |0⟩ + (0.285 + 0.392i) |1⟩
α = cos(θ/2):
0.875
β = e
iϕ
sin(θ/2):
0.285 + 0.392i
Bloch (r_x, r_y, r_z):
(0.50, 0.69, 0.53)