  Motivated by the similarity between adiabatic quantum algorithms and quantum
phase transitions, we study the impact of decoherence on the sweep through a
second-order quantum phase transition for the prototypical example of the Ising
chain in a transverse field and compare it to the adiabatic version of Grovers
search algorithm, which displays a first order quantum phase transition. For
site-independent and site-dependent coupling strengths as well as different
operator couplings, the results show that (in contrast to first-order
transitions) the impact of decoherence caused by a weak coupling to a rather
general environment increases with system size (i.e., number of spins/qubits).
This might limit the scalability of the corresponding adiabatic quantum
algorithm.
