  We consider experimentally feasible chains of trapped ions with pseudo-spin
1/2, and find models that can potentially be used to implement error-resistant
quantum computation. Similar in spirit to classical neural networks, the
error-resistance of the system is achieved by encoding the qubits distributed
over the whole system. We therefore call our system a ''quantum neural
network'', and present a ''quantum neural network model of quantum
computation''. Qubits are encoded in a few quasi-degenerated low energy levels
of the whole system, separated by a large gap from the excited states, and
large energy barriers between themselves. We investigate protocols for
implementing a universal set of quantum logic gates in the system, by adiabatic
passage of a few low-lying energy levels of the whole system. Naturally
appearing and potentially dangerous distributed noise in the system leaves the
fidelity of the computation virtually unchanged, if it is not too strong. The
computation is also naturally resilient to local perturbations of the spins.
