The Molecular Distance Geometry Problem (MDGP) consists in finding an embedding in R3 of a nonnegatively weighted simple undirected graph with the property that the Euclidean distances between embedded adjacent vertices must be the same as the corresponding edge weights. The Discretizable...

Proteins are important molecules that are widely studied in biology. Since their three-dimensional conformations can give clues about their function, an optimal methodology for the identification of such conformations has been researched for many years. Experiments of Nuclear Magnetic Resonance...

The Distance Geometry Problem in three dimensions consists in finding an embedding in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathbb{R}^3}$$</EquationSource> </InlineEquation> of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem...</equationsource></inlineequation>

Grover’s algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical algorithm for finding a local minimum and Grover’s...