  We present a review of quantum computation with neutral atom qubits. After an
overview of architectural options and approaches to preparing large qubit
arrays we examine Rydberg mediated gate protocols and fidelity for two- and
multi-qubit interactions. Quantum simulation and Rydberg dressing are
alternatives to circuit based quantum computing for exploring many body quantum
dynamics. We review the properties of the dressing interaction and provide a
quantitative figure of merit for the complexity of the coherent dynamics that
can be accessed with dressing. We conclude with a summary of the current status
and an outlook for future progress.
