Abstract
We present a scheme for implementing high-fidelity quantum logic gates using the quantum walk of a few interacting bosons on a one-dimensional lattice. The gate operation is carried out by a single compact lattice described by a one-dimensional Bose-Hubbard model with only nearest-neighbor hopping and on-site interactions. We find high-fidelity deterministic logic operations for a gate set (including the CNOT gate) that is universal for quantum information processing. We discuss the applicability of this scheme in light of recent developments in controlling and monitoring cold-atoms in optical lattices, as well as an implementation with realistic nonlinear quantum photonic devices.