  We present a blueprint for building a fault-tolerant universal quantum
computer with Rydberg atoms. Our scheme, which is based on the surface code,
uses individually-addressable optically-trapped atoms as qubits and exploits
electromagnetically induced transparency to perform the multi-qubit gates
required for error correction and computation. We discuss the advantages and
challenges of using Rydberg atoms to build such a quantum computer, and we
perform error correction simulations to obtain an error threshold for our
scheme. Our findings suggest that Rydberg atoms are a promising candidate for
quantum computation, but gate fidelities need to improve before fault-tolerant
universal quantum computation can be achieved.
