Quantum Algorithms and Mathematical Representation of Bio-molecular Solutions for the Hitting-set Problem on a Quantum Computer

In this paper, it is demonstrated that quantum implementation of bio-molecular solutions to compute the number of elements in each hitting-set in an instance of the hitting-set problem could be considered as the oracle work in Grover’s algorithm, i.e., the target state labeling, preceding Grover’s searching steps. Finally, for testing our theory, a three-qub it nuclear magnetic resonance (NMR) experiment of solving the simplest hitting-set problem is performed.