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Finding cliques by quantum adiabatic evolution

Andrew M. Childs·Edward Farhi·Jeffrey Goldstone·Sam Gutmann
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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.

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Andrew M. Childs, Edward Farhi, Jeffrey Goldstone, Sam Gutmann. 2000-12-19. Finding cliques by quantum adiabatic evolution. https://doi.org/10.26421/qic2.3

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