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We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single- and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of for each operation. Current limitations and possible approaches to further improvement of the device are discussed.