Finding cliques by quantum adiabatic evolution
Quantum Physics
2018-12-20 v1
Abstract
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.
Cite
@article{arxiv.quant-ph/0012104,
title = {Finding cliques by quantum adiabatic evolution},
author = {Andrew M. Childs and Edward Farhi and Jeffrey Goldstone and Sam Gutmann},
journal= {arXiv preprint arXiv:quant-ph/0012104},
year = {2018}
}
Comments
11 pages, 4 EPS figures, REVTeX