Quantum optimization for solving nonconvex problem

This paper presents a quantum optimization problem and solid-state quantum computing architectures. Quantum approach to global optimization and NP-complete problems are considered. Our approach to global optimization based on quantum mechanical entanglement, quantum resonant tunneling, cellular automaton and geometric control methods. A quantum optimization algorithm combines the properties of classical simulated annealing with the possibility of quantum tunneling between the minima. Quantum computation exploits the property of quantum states to implement quantum parallelism for global nonconvex optimization problem. This paper considers new mathematical models of classical (CL) and quantum-mechanical lattices (QML). System-theoretic results on the observability, controllability and minimal realizability theorems are formulated for CL. The cellular dynamaton (CD) based on quantum oscillators is presented. We investigate the conditions when stochastic resonance can occur through the interaction of dynamical neurons with intrinsic deterministic noise and an external periodic control.