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Quantum phenomena of interest in connection with applications to computation and communication often involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schrödinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed. [ABSTRACT FROM AUTHOR]

Many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control. Examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy. Likewise, cyclic processes are prevalent in nature and the idea of a pattern generator is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration. In this paper, we develop a linkage between the use of cyclic processes and the control of nonholonomic systems, emphasizing the problem of achieving stable regulation. The discussion brings to the fore characteristic phenomena that distinguish the regulation problem for such strongly nonlinear systems from the more commonly studied linear feedback regulators. Finally, we compare this approach to controlling nonholonomic systems to another approach based on the idea of an open-loop approximate inverse as discussed in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we show that when it is possible to use feedback in the specification of "motor programs," the length of the descriptions of the instruction sequences for carrying out a given task can be reduced by a factor that reflects the richness of the available feedback signals. The model on which this work is based is that of a finite automaton, modified in such a way that instruction processing is akin to the way in which difference or differential equations "process" piecewise constant inputs. In terms of such "free-running" automata, we show that when feedback is available the length of the shortest description can be reduced by a factor depending on the ratio of the size of the entire state space to the size of the set of states for which feedback is locally effective. [ABSTRACT FROM AUTHOR]

Addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurement. Proposed control design methodology which relies on the possibility of changing the sensitivity of the quantizer; Interconnection between the equation and given system; Global asymptotic stability yielded by the system.

Describes a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. Monotemperaturic systems' relationship with Lyapunov functions; Stochastic optimal control problems in the case of quantized feedback.

Examines the stabilization of feedback control systems with finite communication bandwidth constraints. Issue of coding and communication protocol; Introduction of the containability concept; Inequality equation involving the communication data rate and the rate of change of the state of the system.

Provides information on the investigation of a state estimation problem involving finite communication capacity constraints. Detailed information on the formulation of the problem; Information on the coder-estimator sequence; Conclusion reached.