  Single atoms in dipole microtraps or optical tweezers have recently become a
promising platform for quantum computing and simulation. Here we report a
detailed theoretical analysis of the physics underlying an implementation of a
Rydberg two-qubit gate in such a system -- a cornerstone protocol in quantum
computing with single atoms. We focus on a blockade-type entangling gate and
consider various decoherence processes limiting its performance in a real
system. We provide numerical estimates for the limits on fidelity of the
maximally entangled states and predict the full process matrix corresponding to
the noisy two-qubit gate. Our methods and results may find implementation in
numerical models for simulation and optimization of neutral atom based quantum
processors.
