We demonstrate an implementation scheme for constructing quantum gates using
unitary evolutions of the one-dimensional spin-J ferromagnetic XXZ chain. We present
numerical results based on simulations of the chain using the time-dependent DMRG method
and techniques from optimal control theory. Using only a few control parameters, we find
that it is possible to implement one- and two-qubit gates on a system of spin-3/2 XXZ
chains, such as Not, Hadamard, Pi-8, Phase, and C-Not, with fidelity levels exceeding 99%.