  Adiabatic quantum algorithms represent a promising approach to universal
quantum computation. Whilst in a closed system these algorithms are limited by
avoided level crossings, where the gap becomes exponentially small in the
system size, their robustness in open systems remains unresolved. We study the
dynamics in the proximity of such an avoided level crossing associated with the
adiabatic quantum search algorithm in a quantum system that is coupled to a
generic environment. At zero temperature, we find that the algorithm remains
scalable provided the noise spectral density of the environment decays
sufficiently fast at low frequencies. At finite temperature, however,
scattering processes render the algorithm inefficient and no quantum speedup
can be achieved. Owing to the generic nature of our model, we expect our
results to be widely applicable to other adiabatic quantum algorithms.
