  Designing a good transfer channel for arbitrary quantum states in spin chains
implies optimizing a cost function, usually the averaged fidelity of
transmission. The fidelity of transmission measures how much the transferred
state resembles the state prepared at the beginning of the transfer protocol.
When averaged over all the possible initial states, the figure of merit
quantifies the quality of the protocol. There are proposals for optimizing a
given Hamiltonian to accomplish a particular task. The transfer of quantum
states is one of them. In particular, we consider the design of Heisenberg spin
chains using a genetic algorithm. This very efficient algorithm allows us to
study different properties of Hamiltonians with good to excellent transfer
ability. One apparent drawback of using a random search method is that it
results in exchange coefficient strengths that change abruptly from site to
site. Modifying the cost function, we obtain Hamiltonians with exchange
coefficients varying smoothly along the chain length. Our results show that the
smoothed Hamiltonians have the same, or less, transfer ability than the rough
ones, and both kinds show similar robustness against static disorder. By
studying the statistical properties of the eigenvalues of Hamiltonians with
varying transfer abilities, we determine the ensemble of random matrices to
which the spectra belong.
