Single-Qubit RB: 3D Bloch Sphere Trajectory

This is the same real randomized-benchmarking protocol as the 2D version, viewed from inside the state space instead of from the decay curve: a 3D Bloch sphere shows one example trial's exact path as a random string of Clifford gates carries the qubit's state across the sphere, followed by the exact inverse of that whole sequence, which would return the state precisely to the north pole in the absence of noise. With real per-gate depolarizing noise switched on, the return point sits inside the sphere at a radius set by exactly how much noise accumulated — an honest, computed consequence of the simulation, not a scripted animation. A live decay-curve panel below keeps fitting the same exponential to an independently running batch of random sequences, so you can see the microscopic single-trajectory picture and the macroscopic statistical fit side by side.