Qubit Bloch Sphere Simulator

Every pure state of a single qubit can be drawn as an arrow from the center of a unit sphere — the Bloch sphere — with the north pole representing |0⟩ and the south pole |1⟩. This simulator lets you apply the Hadamard, Pauli-X, Pauli-Z and an adjustable phase gate to a qubit and watch its state vector rotate in real time in 3D, while readouts track the polar angle θ, azimuthal phase φ, and the resulting measurement probabilities P(|0⟩) and P(|1⟩). Toggle decoherence to see the vector's length shrink from the sphere's surface (a pure state) toward its center (a fully mixed state), the same process that limits every real quantum computing platform and motivates quantum error correction.