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Systems & Control Letters

Reachable set of operators on controlled open quantum systems in a Markovian environment

Haidong Yuan

Published Sep 26, 2012• 8 citations
Publisher
DOI
10.1016/j.sysconle.2012.08.001

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Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.
In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature T ≥ 0. The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved:(i)permutations within the simplex,(ii)contractions by a dissipative one-parameter semigroup. Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. We completely characterize the case T = 0 and present inclusions for T > 0.