  We present a scheme for universal quantum computing using XY Heisenberg spin
chains. Information is encoded into packets propagating down these chains, and
they interact with each other to perform universal quantum computation. A
circuit using g gate blocks on m qubits can be encoded into chains of length
$O(g^{3+\delta} m^{3+\delta})$ for all $\delta >0$ with vanishingly small
error.
