title: Quantum algorithms and mathematical formulations of biomolecular solutions of the vertex cover problem in the finite-dimensional hilbert space.
abstract: 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.
authors.forename: Weng-Long
authors.initials: WL
authors.lastname: Chang
authors.forename: Ting-Ting
authors.initials: TT
authors.lastname: Ren
authors.forename: Mang
authors.initials: M
authors.lastname: Feng
mesh_terms: D000465:Algorithms; D004247:DNA; D009682:Magnetic Resonance Spectroscopy; D011789:Quantum Theory
chemical_list: D004247:DNA