  We present a complete architecture for scalable quantum computation with
ultracold atoms in optical lattices using optical tweezers focused to the size
of a lattice spacing. We discuss three different two-qubit gates based on local
collisional interactions. The gates between arbitrary qubits require the
transport of atoms to neighboring sites. We numerically optimize the
non-adiabatic transport of the atoms through the lattice and the intensity
ramps of the optical tweezer in order to maximize the gate fidelities. We find
overall gate times of a few 100 us, while keeping the error probability due to
vibrational excitations and spontaneous scattering below 10^3. The requirements
on the positioning error and intensity noise of the optical tweezer and the
magnetic field stability are analyzed and we show that atoms in optical
lattices could meet the requirements for fault-tolerant scalable quantum
computing.
