%0 Journal Article
%D 2000
%T Finding cliques by quantum adiabatic evolution
%A Andrew M. Childs
%A Edward Farhi
%A Jeffrey Goldstone
%A Sam Gutmann
%X 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.
%8 2000/12/19
%G eng
%U http://arxiv.org/abs/quant-ph/0012104v1
%! Quantum Information and Computation 2