I will explain (assuming zero background on quantum comp.!) our recent
result which shows that "adiabatic quantum computation", which has
recently attracted considerable attention in the scientific community, is
equivalent in computational power to the conventional model of quantum
computation. This clarifies the computational power of the adiabatic
model, and means that quantum computation can be fully studied in the
adiabatic paradigm.

The definition of Adiabatic computation, which I will explain in
full detail, conveys why it is an attractive model from a theoretical
point of view: its main objects are very reminiscent of those used in
rapidly mixing Markov chains, namely principal eigenvectors and non
negligible spectral gaps. Our result raises the hope for borrowing tools
from the extensive scientific literature on spectral gap analysis to
attack the difficult challenges in quantum computation, and also makes
these challenges accessible to a wider audience.

Joint works with van Dam, kempe, Landau, Lloyd, Regev and Ta-Shma.