On the relevance of avoided crossings away from quantum critical point to the complexity of quantum adiabatic algorithm

@article{Knysh2010OnTR,
title={On the relevance of avoided crossings away from quantum critical point to the complexity of quantum adiabatic algorithm},
author={Sergey Knysh and Vadim N. Smelyanskiy},
journal={CoRR},
year={2010},
volume={abs/1005.3011}
}

Two recent preprints [B. Altshuler, H. Krovi, and J. Roland, “Quantum adiabatic optimization fails for random instances of NP-complete problems”, arXiv:0908.2782 and “Anderson localization casts clouds over adiabatic quantum optimization”, arXiv:0912.0746] argue that random 4th order perturbative corrections to the energies of local minima of random instances of NP-complete problem lead to avoided crossings that cause the failure of quantum adiabatic algorithm (due to exponentially small gap… CONTINUE READING