  We investigate continuous-time quantum walks of two indistinguishable
particles (bosons, fermions or hard-core bosons) in one-dimensional lattices
with nearest-neighbour interactions. The two interacting particles can undergo
independent- and/or co-walking dependent on both quantum statistics and
interaction strength. We find that two strongly interacting particles may form
a bound state and then co-walk like a single composite particle with
statistics-dependent propagation speed. Such an effective single-particle
picture of co-walking is analytically derived in the context of degenerate
perturbation and the analytical results are well consistent with direct
numerical simulation. In addition to implementing universal quantum computation
and observing bound states, two-particle quantum walks offer a novel route to
detecting quantum statistics. Our theoretical results can be examined in
experiments of light propagations in two-dimensional waveguide arrays or
spin-impurity dynamics of ultracold atoms in one-dimensional optical lattices.
