  We present a method for encoding and transporting qubits within a dimerized
Heisenberg spin-1/2 chain. Logical qubits are localized at the domain walls
that separate the two possible dimerized states. The domain walls can be moved
to produce "flying spin qubits". The topological nature of these states makes
them stable against a wide class of perturbations. Pairs of domain walls can be
used to generate Einstein-Podolsky-Rosen pairs of entangled qubits. We discuss
speed limitations within an exactly solvable three-spin model and describe a
possible physical realization using quantum dot arrays.
