Fast nuclear-spin entangling gates compatible with large-scale atomic arrays

Fast nuclear-spin entangling gates of divalent atoms can be realized with one global laser pulse when ₙ<, where ₙ is the Zeeman-splitting-dominated frequency difference between the two clock-Rydberg transitions of the two qubit states and is the maximal Rabi frequency. The condition ₙ< and the sensitivity of Rydberg-state energy to magnetic fluctuation demand the magnetic field to be weak, making the gate compatible with large-scale atomic arrays because weaker magnetic fields can be smoother in a large qubit array. The gate can have a high fidelity for the decoherence of Rydberg states, which limits the gate fidelity and grows with 1/, can be mitigated with easily attainable large.