



01120nas a2200145   4500008004100000245005100041210005100092260001500143520069100158100002300849700001800872700002300890700001700913856004400930       2000                        eng d00aFinding cliques by quantum adiabatic evolution0 aFinding cliques by quantum adiabatic evolution  c2000/12/193 a  Quantum adiabatic evolution provides a general technique for the solution of
combinatorial search problems on quantum computers. We present the results of a
numerical study of a particular application of quantum adiabatic evolution, the
problem of finding the largest clique in a random graph. An n-vertex random
graph has each edge included with probability 1/2, and a clique is a completely
connected subgraph. There is no known classical algorithm that finds the
largest clique in a random graph with high probability and runs in a time
polynomial in n. For the small graphs we are able to investigate (n <= 18), the
quantum algorithm appears to require only a quadratic run time.
1 aChilds, Andrew, M.1 aFarhi, Edward1 aGoldstone, Jeffrey1 aGutmann, Sam  uhttp://arxiv.org/abs/quant-ph/0012104v1