  We study the quantum walks of two interacting spin-1 bosons. We derive an
exact solution for the time-dependent wave function that describes the
two-particle dynamics governed by the one-dimensional spin-1 Bose-Hubbard
model. We show that propagation dynamics in real space and mixing dynamics in
spin space are correlated via the spin-dependent interaction in this system.
The spin-mixing dynamics has two characteristic frequencies in the limit of
large spin-dependent interactions. One of the characteristic frequencies is
determined by the energy difference between two bound states, and the other
frequency relates to the cotunneling process of a pair of spin-1 bosons.
Furthermore, we numerically analyze the growth of the spin correlations in
quantum walks. We find that long-range spin correlations emerge showing a clear
dependence on the sign of the spin-dependent interaction and the initial state.
