Quantum Algorithms and Mathematical Formulations of Biomolecular Solutions of the Vertex Cover Problem in the Finite-Dimensional Hilbert Space
Weng-Long Chang, Ting-Ting Ren, Mang Feng · IEEE Transactions on NanoBioscience · 2014
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.