Abstract: Embodiments of the disclosed invention include optimization methods and systems that receive a mathematical description of a system, in symbolic form, that includes decision variables of various types, including real-number-valued, integer-valued, and Boolean-valued decision variables, and that may also include a variety of constraints on the values of the decision variables, including inequality and equality constraints. The objective function and constraints are incorporated into a global objective function. The global objective function is transformed into a system of differential equations in terms of continuous variables and parameters, so that polynomial-time methods for solving differential equations can be applied to calculate near-optimal solutions for the global objective function.

Abstract: A method and apparatus for quantum computing. A computer-program source code, data, and unsubstantiated output variables are converted into a class of computable functions by a program compiler. The computable functions are encoded, and a continualization method is applied to the encoded functions to determine a first-order, time-dependent, differential equation. Variational calculus is employed to construct a Lagrangian whose minimum geodesic is the solution for the first-order, time-dependent, differential equation. The Lagrangian is converted into a quantum, canonical, Hamiltonian operator which is realized as an excitation field via an excitation generator. The excitation field is repeatedly applied to a quantum processor consisting of a lattice of polymer nodes to generate an intensity-versus-vibrational-frequency spectrum of the lattice nodes.

Abstract: Embodiments of the disclosed inventinn include optimization methods and systems that receive a mathematical description of a system, in symbolic form, that includes decision variables of various types, including real-number-valued, integer-valued, and Bloolean-valued decision variables, and that may also include a variety of constraints on the values of the decision variables, including inequality and equality constraints. The objective function and constraints are incorporated into a global objective function. The global objective function is transformed into a system of differential equations in terms of continuous variables and parameters, so that polynomial-time methods for solving differential equations can be applied to calculate near-optimal solutions for the global objective function.