  Using a global optimization algorithm, interchange coupling distributions are
obtained for chains of quantum spins. The couplings give the magnitude of the
interaction between the spins of the chain, both chains with Heisenberg
Hamiltonian and XXZ type anisotropic Hamiltonian are considered. These
couplings allow the chains to be used as channels to transmit quantum states
according to the simplest transmission protocol. It is analyzed under which
conditions it is possible to obtain very high transmission fidelities, both as
a function of the arrival time and the maximum intensity allowed for the
couplings. Special emphasis is placed on finding coupling sets that allow fast
transmission, with short arrival times on the order of $N$, where $N$ is the
number of spins in the chain. The stability of the chains as transmission
channels is analyzed also when the couplings are subject to static disorder.
Finally it is shown that the transmission fidelity at different arrival times
shows scaling properties.
