Coupled dynamics of spin qubits in optical dipole microtraps

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.