Abstract
The objective of this paper is to create a new kind of dynamical systems—a quantum-classical hybrid—that would preserve superposition and entanglement of random solutions while allowing one to measure their state variables by using classical methods. Such an optimal combination of characteristics is a perfect match for quantum-inspired computing. The model is represented by a modified Madelung equation in which the quantum potential is replaced by a different, specially chosen “computational” potential. As a result, the dynamics attains both quantum and classical properties. Similarities and differences of the proposed model with quantum systems are outlined. As an application, an algorithm for the global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithms is very simple: based on the quantum-inspired maximizer, introduce a positive function to be maximized as the probability density to which the solution is attracted. Then, the larger value of this function will have the higher probability to appear. Special attention is paid to the simulation of integer programming, NP-complete problems and information retrieval.
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