Collisional gates in optical superlattices recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast $\sqrt{\mathrm{SWAP}}$ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasiharmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for $\sqrt{\mathrm{SWAP}}$ and generates entanglement. We employ a continuum, time-dependent Schrödinger-equation simulation that goes beyond a two-site Fermi-Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in $\sim 21\mu \mathrm{s}$, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities $\gtrsim 99\%$. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.

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• Cold gases in optical lattices
• Quantum gates
• Ultracold collisions
• Ultracold gases