  Incorporating protection against quantum errors into adiabatic quantum
computing (AQC) is an important task due to the inevitable presence of
decoherence. Here we investigate an error-protected encoding of the AQC
Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian
only involves total spin operators of the ensembles, offering a simpler route
towards error-corrected quantum computing. Our scheme is particularly suited to
neutral atomic gases where it is possible to realize large ensemble sizes and
produce ensemble-ensemble entanglement. We identify a critical ensemble size
$N_{\mathrm{c}}$ where the nature of the first excited state becomes a single
particle perturbation of the ground state, and the gap energy is predictable by
mean-field theory. For ensemble sizes larger than $N_{\mathrm{c}}$, the ground
state becomes protected due to the presence of logically equivalent states and
the AQC performance improves with $N$, as long as the decoherence rate is
sufficiently low.
