Quantum computing in control and optimization

ABSTRACT This paper deals with the progress made in applications of quantum computing in control and optimization..It concentrates on applying the geometric technique in order to investigate a “nite control problem of a two-level quantum system, resonance control of a three-level system, simulation of bilinear quantum control systems,and optimal control using the Bellman principle. We show that a quantum object described by a Schr¨ odingerequation can be controlled in an optimal way by electromagnetic modes. We also demonstrate an applicationof these techniques and an algebra-geometric approach to the study of dynamic processes in nonlinear systems.The information processing by means of controlled quantum lattices is discussed: we present new mathematicalmodels of classical (CL) and quantum-mechanical lattices (QML) and their application to information processing.system-theoretical results on the observability, controllability and minimal realizability theorems are formulatedfor cl. The cellular dynamaton (CD) based on quantum oscillators is presented. Cellulars quantum compu-tational search procedure can provide the basis for implementing adaptive global optimization algorithms. Abrief overview of the procedure is given and a framework called lattice adaptive search is set up. A method ofYatsenko and one introduced by the authors “t into this framework and are compared.Keywords: Quantum computing, control, global optimization, random search