Trapped-Ion Mølmer–Sørensen Gate Simulator

The Mølmer–Sørensen (MS) gate is the workhorse two-qubit entangling operation of real trapped-ion quantum computers. This simulator renders a linear Paul trap holding two ions and drives their shared motional mode with a bichromatic laser field, tracing out the resulting spin-dependent phase-space loop in real time. Adjust the drive strength Ω_eff and sideband detuning δ, choose how many loops the gate completes, and watch the ions' motional excitation, the geometric entangling phase, and the resulting |gg⟩/|ee⟩ Bell-state populations evolve together — with the phonon number returning to zero exactly when the phase-space loop closes, the signature that makes this gate robust against motional heating.