08-05-2012, 04:02 PM
Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
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INTRODUCTION
QUANTUM feedback control involves the interconnection
of two systems (the quantum plant and the controller)
in such a way that the plant-controller system achieves
desired performance specifications. The controller may be a
quantum system, a classical system (i.e., not quantum), or a
mixture of the two. When the controller is a classical system,
the feedback loop involves measurement, and hence is referred
to as measurement feedback; see [2]–[4], [13], [21], [23], [28],
[40], [44], [46], and [48]. Measurement feedback necessarily
involves the loss of quantum coherence in the feedback loop.
Measurement feedback control has been applied to the theoretical
study of spin localization [3],
Closed-Loop Plant-Controller System
Consider two quantum linear systems: , the plant to be controlled,
coupled to , the controller, as shown in Fig. 7. This
feedback system involves both direct and indirect coupling between
the plant and the controller. While the feedback architecture
will be fixed, the parameters defining the controller (which
includes the couplings) will be synthesized using and LQG
performance criteria.
COHERENT FEEDBACK CONTROLLER SYNTHESIS
So far, we have looked at some basic performance characteristics
of linear quantum systems (stability, passivity, gain), and
in particular, we have seen how direct coupling can influence
behavior. In this section, we turn to the problem of including
direct couplings in systematic controller design methodologies.
Using direct couplings in design is natural from the physical
point of view and has been considered in [24]. Our interest here
to design direct and indirect couplings to optimize specific performance
criteria. In general, explicit solutions are not known,
and optimization algorithms are used.
CONCLUSION
In this paper, we have investigated the influences and uses
of indirect and direct couplings in coherent feedback control of
linear quantum stochastic feedback systems. In particular, we
have shown that the uses of direct coupling can have beneficial
performance consequences, and that the design of direct couplings
may be achieved in a systematic, optimization-based approach.
The results of this paper will help to build an integrated,
first-principles methodology for coherent quantum control. Future
work will include further practical application of the synthesis
method of direct couplings in the field of quantum optics.