  Adiabatic quantum computation has recently attracted attention in the physics
and computer science communities, but its computational power was unknown. We
describe an efficient adiabatic simulation of any given quantum algorithm,
which implies that the adiabatic computation model and the conventional quantum
computation model are polynomially equivalent. Our result can be extended to
the physically realistic setting of particles arranged on a two-dimensional
grid with nearest neighbor interactions. The equivalence between the models
provides a new vantage point from which to tackle the central issues in quantum
computation, namely designing new quantum algorithms and constructing fault
tolerant quantum computers. In particular, by translating the main open
questions in the area of quantum algorithms to the language of spectral gaps of
sparse matrices, the result makes these questions accessible to a wider
scientific audience, acquainted with mathematical physics, expander theory and
rapidly mixing Markov chains.
