Controlled-SWAP gates by tuning of interfering transition pathways in neutral atom arrays

Neutral-atom quantum processors employ Rydberg blockade for multiqubit phase operations but lack similar native exchange and conditional exchange gates, which are essential primitives for state verification, fermionic and XY-model simulation, and efficient routing in large qubit arrays. We demonstrate that by lifting the degeneracy between interfering transition pathways, a single Rydberg-excited atom can control state exchange between pairs of atoms. Using this mechanism, we realize a direct controlled-SWAP (Fredkin) operation with more than 99% fidelity and an order-of-magnitude reduction in circuit depth and reduced exposure to decay and decoherence of Rydberg state components compared with decomposed implementations. The mechanism operates robustly under Doppler broadening at 150 μK and realistic laser-intensity noise and extends naturally to an entire family of useful gates, including multi-control conditional exchanges C$_k$-SWAP and conditional multiplexed SWAP gates. By incorporating controlled exchange operations as native physical operations on neutral atoms, our work provides multiqubit gates that enable higher-order state-verification protocols, occupation-dependent simulations, and conditional routing across optical lattices.