Non-Markovian decoherence in the adiabatic quantum search algorithm

We consider an adiabatic quantum algorithm (Grover's search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. It turns out that the scalability of the adiabatic quantum algorithm just depends on the infrared behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field, for example, does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic.