  A uniformly coupled double quantum Hamiltonian for a spin chain has recently
been implemented experimentally. We propose a method for the determination of
initial quantum states that will provide perfect or near-perfect state
transmission for an arbitrary Hamiltonian including this one. By calculating
the eigenvalues and eigenvectors of a unitary operator obtained from the free
evolution plus an exchange operator, we find that the double quantum
Hamiltonian spin chain will support a three-spin initial encoding that will
transfer along the chain with remarkably high fidelity. The fidelity is also
found to decrease very slowly with increasing chain length. In addition, we are
able to explain previous results showing exceptional transfer using this
method.
