  Analog models of quantum information processing, such as adiabatic quantum
computation and analog quantum simulation, require the ability to subject a
system to precisely specified Hamiltonians. Unfortunately, the hardware used to
implement these Hamiltonians will be imperfect and limited in its precision.
Even small perturbations and imprecisions can have profound effects on the
nature of the ground state. Here we consider an imperfect implementation of
adiabatic quantum optimization and show that, for a widely applicable random
control noise model, quantum stabilizer encodings are able to reduce the
effective noise magnitude and thus improve the likelihood of a successful
computation or simulation. This reduction builds upon two design principles:
summation of equivalent logical operators to increase the energy scale of the
encoded optimization problem, and the inclusion of a penalty term comprising
the sum of the code stabilizer elements. We illustrate our findings with an
Ising ladder and show that classical repetition coding drastically increases
the probability that the ground state of a perturbed model is decodable to that
of the unperturbed model, while using only realistic two-body interaction.
Finally, we note that the repetition encoding is a special case of quantum
stabilizer encodings, and show that this in principle allows us to generalize
our results to many types of analog quantum information processing, albeit at
the expense of many-body interactions.
