Neutral atom qubits encode information in the internal states of individual neutral atoms (commonly rubidium or cesium) trapped in tightly focused laser beams called optical tweezers. Arrays of tweezers can be arranged into arbitrary two- or three-dimensional geometries, which gives this platform unusual flexibility in qubit connectivity compared to the fixed layouts of a chip. Qubit states are typically encoded either in hyperfine ground states or, for two-qubit gates, temporarily excited to Rydberg states.
Single-qubit gates are driven by resonant laser or microwave fields coupling the two hyperfine ground states used as $\lvert 0 \rangle$ and $\lvert 1 \rangle$. Two-qubit gates exploit the Rydberg blockade: when one atom is excited to a high-lying Rydberg state, the resulting strong dipole-dipole interaction shifts the Rydberg energy level of a nearby atom enough to prevent it from also being excited, entangling the pair.
$$H = \hbar \sum_i \frac{\Omega_i}{2} \left( \lvert g_i \rangle \langle r_i \rvert + \lvert r_i \rangle \langle g_i \rvert \right) - \hbar \sum_i \Delta_i \lvert r_i \rangle \langle r_i \rvert + \sum_{i<j} \frac{C_6}{r_{ij}^6} \lvert r_i \rangle \langle r_i \rvert \otimes \lvert r_j \rangle \langle r_j \rvert$$
$\Omega_i$ and $\Delta_i$ are the Rabi frequency and detuning of the laser driving atom $i$ from the ground state $\lvert g_i \rangle$ to the Rydberg state $\lvert r_i \rangle$, and the last term is the van der Waals interaction between atoms in the Rydberg state, scaling as $1/r^6$ with interatomic distance $r_{ij}$ and coefficient $C_6$. This interaction term is the source of the Rydberg blockade.
Because atoms are held in individually programmable tweezer arrays, this platform has demonstrated some of the largest qubit counts of any technology, with hundreds of atoms arranged and rearranged mid-circuit using movable tweezers. The main challenges are gate fidelity, since Rydberg states are more sensitive to laser noise and atomic motion than ground states, and atom loss, since a trapped atom can occasionally escape the tweezer and needs to be reloaded.