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In this paper, it is demonstrated that solving an instance of the vertex cover problem of any graph G with m edges and n vertices can be implemented by Hadamard gates, NOT gates, CNOT gates, CCNOT gates, Grover's operators, and quantum measurements on a quantum computer. To test our theory, an NMR (nuclear magnetic resonance) experiment for the simplest vertex-cover problem is also performed.
We demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented by our proposed quantum algorithm on the quantum machine proposed by Deutsch. Moreover, we also prove that the logic computation by the bio-molecular operations proposed by Adleman can be implemented by quantum gates (for example, the Hadamard gate,...
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