English

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.

Keywords

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