2010/02/23 by Markku Nihtilä, Nihtilä, Markku
Mathematics · Physics and Astronomy · #49J15 #81Q93 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #math-ph #math.MP #math.OC #msc:49J15 #msc:81Q93
paper · pdf · doi:10.48550/arxiv.1002.4260
Theoretical part of this paper without simulation figures appears in the CD-preprint of Fourth International Symposium on Communications, Control and Signal Processing, Limassol, Cyprus, March 3-5, 2010 (ISCCSP 2010)
arxiv created 2010/02/23 · arxiv updated 2010/02/26
In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A four-dimensional real-variable differential equation model is constructed from the complex-valued two-level model describing the wave function of the system. The state transition matrix of the model is constructed via the Wei-Norman technique and Lie algebraic methodology. The idea of parametrization using flatness-based control, is applied to construct feasible input--output pairs of the model. This input drives the state of the system from the given initial state to the given final state in a finite time producing the corresponding output of the pair. The population transfer is obtained by nullifying part of the state vector via careful selection of the parameter functions. A preliminary simulation study completes the paper.