Quantum computing with atomic qubit arrays: confronting the cost of connectivity

These notes present a review of the status of quantum computing with arrays of neutral atom qubits, an approach which has demonstrated remarkable progress in the last few years. Scaling digital quantum computing to qubit counts and control fidelities that will enable solving outstanding scientific questions, and provide commercial value, is an outstanding challenge, not least because of the requirement of connecting and entangling distant qubits. Long-range Rydberg gates and physical motion outfit atomic qubit arrays with tools for establishing connectivity. These tools operate on different timescales and with distinct levels of parallelization. We analyze several prototypical architectures from the perspective of achieving fast connectivity for circuits with large scale entanglement, as well as fast cycle times for measurement based quantum error correcting codes. Extending Rydberg interactions to multiple atomic species has emerged as a promising route to achieving this latter requirement.