Quantum dynamics, control

There are many other quantum dynamics control protocols that we have not discussed see Ref. 10 for descriptions and a discussion of those that fall into the shortcuts to adiabaticity category, and Refs 1,2 for descriptions and discussion of other control methodologies. 

Warren W S, Rabitz H and Dahleh M 1993 Coherent control of quantum dynamics the dream is alive Science 259 1581... 

Considering any of these paradigms, a minimal goal for toy models would be to manipulate the quantum dynamics of a small number of spin levels , and that requires a known and controlled composition of the wavefunction, sufficient isolation and a method for coherent manipulation. As illustrated in Figure 2.13, the first few magnetic states of the system are labelled and thus assigned qubit values. The rest of the spectrum is outside of the computational basis, so one needs to ensure that these levels are not populated during the coherent manipulation. 

The ar tide is organized as follows. We will begin with a discussion of the various possibilities of dynamical description, clarify what is meant by nonlinear quantum dynamics , discuss its connection to nonlinear classical dynamics, and then study two experimentally relevant examples of quantum nonlinearity - (i) the existence of chaos in quantum dynamical systems far from the classical regime, and (ii) real-time quantum feedback control. 

To illustrate an application of nonlinear quantum dynamics, we now consider real-time control of quantum dynamical systems. Feedback control is essential for the operation of complex engineered systems, such as aircraft and industrial plants. As active manipulation and engineering of quantum systems becomes routine, quantum feedback control is expected to play a key role in applications such as precision measurement and quantum information processing. The primary difference between the quantum and classical situations, aside from dynamical differences, is the active nature of quantum measurements. As an example, in classical theory the more information one extracts from a system, the better one is potentially able to control it, but, due to backaction, this no longer holds true quantum mechanically. 

CONTROLLING QUANTUM DYNAMICS WITH ASSISTED ADIABATIC PROCESSES... 

We now consider control of the quantum dynamics of a one-component gas composed of N particles with mass m and charge q without spin. We derive the driving potential and the vector potential, which generate... 

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