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Finding cliques by quantum adiabatic evolution
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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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Cited by 1 Pith paper
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Efficient Maximum Clique Detection via Grover's Algorithm with Real-time Global Size Tracking
A proposed Grover-based maximum clique solver claims O(sqrt(2^n)) iterations and O(1) measurements by pre-encoding the clique size, but the pre-encoding itself costs exponentially many gates and is excluded from the h...
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