Qubit Gates on the Bloch Sphere

Every single-qubit state in quantum computing can be pictured as an arrow on the Bloch sphere, and every quantum gate is a rotation of that arrow. This simulator renders a real 3D Bloch sphere and lets you apply the standard gate set — Hadamard, Pauli X/Y/Z, S and T — to a qubit initialised in |0⟩, watching the state vector rotate exactly as the underlying 2×2 unitary matrices dictate. A continuous phase-rotation slider shows gates as one point on a smooth family of rotations, live readouts track the polar and azimuthal Bloch angles plus the Born-rule measurement probabilities, and the Measure button samples a real probabilistic outcome and collapses the state to the corresponding pole.