Dynamical Decoupling: Spin Echo vs CPMG

A qubit prepared in superposition loses coherence when it drifts out of phase with the reference clock — either because every copy in an ensemble sees a slightly different static field (inhomogeneous broadening, T2*) or because the field itself fluctuates in time. This simulator renders a real ensemble of ~240 such "isochromats" as points fanning around the equator of a 3D Bloch sphere, integrating each one's phase under a chosen static disorder and a fluctuating Ornstein–Uhlenbeck noise bath. Switching between Free Induction Decay, a single Hahn echo, and 4- or 8-pulse CPMG sequences shows, live, how inserting π-pulses reverses accumulated dephasing and refocuses the ensemble — the actual dynamical-decoupling technique used to extend coherence time in real quantum hardware.