  Arrays of optically trapped atoms excited to Rydberg states have recently
emerged as a competitive physical platform for quantum simulation and
computing, where high-fidelity state preparation and readout, quantum logic
gates and controlled quantum dynamics of more than 100 qubits have all been
demonstrated. These systems are now approaching the point where reliable
quantum computations with hundreds of qubits and realistically thousands of
multiqubit gates with low error rates should be within reach for the first
time. In this article we give an overview of the Rydberg quantum toolbox,
emphasizing the high degree of flexibility for encoding qubits, performing
quantum operations and engineering quantum many-body Hamiltonians. We then
review the state-of-the-art concerning high-fidelity quantum operations and
logic gates as well as quantum simulations in many-body regimes. Finally, we
discuss computing schemes that are particularly suited to the Rydberg platform
and some of the remaining challenges on the road to general purpose quantum
simulators and quantum computers.
