  We propose a two-qubit collisional phase gate that can be implemented with
available atom chip technology, and present a detailed theoretical analysis of
its performance. The gate is based on earlier phase gate schemes, but uses a
qubit state pair with an experimentally demonstrated, very long coherence
lifetime. Microwave near-fields play a key role in our implementation as a
means to realize the state-dependent potentials required for conditional
dynamics. Quantum control algorithms are used to optimize gate performance. We
employ circuit configurations that can be built with current fabrication
processes, and extensively discuss the impact of technical noise and
imperfections that characterize an actual atom chip. We find an overall
infidelity compatible with requirements for fault-tolerant quantum computation.
