Mølmer–Sørensen Gate: Phase-Space Loop (2D)

Trapped-ion quantum processors entangle qubits without ever letting them touch: two ions in a linear trap share one collective vibration, and a pair of off-resonant laser tones pushes that shared "phonon bus" around a loop in phase space whose direction depends on the ions' spins. This 2D companion renders a top-down ion-chain schematic alongside a full pannable, zoomable phase-space plot of α(t), so you can watch the loop open, sweep out a geometric phase, and close again — the exact mechanism behind the Mølmer–Sørensen gate used in real trapped-ion hardware (IonQ, Quantinuum). Tune the sideband detuning and coupling strength, flip the spin pair to mirror the loop, and track the accumulated entangling phase against the π/4 target for a maximally entangling two-qubit gate.