Protocols of coherent motion control for an interaction-driven Rydberg gate

Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below $10^{-4}$, heat the atom by less than~$\Delta n = 0.01$, while being robust to alignment errors of the potential up to $50$~nm and thermal excitation up to $\bar{n} = 3$. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only $\sim 10$~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.