687 research outputs found
Decoherence Control in Open Quantum System via Classical Feedback
In this work we propose a novel strategy using techniques from systems theory
to completely eliminate decoherence and also provide conditions under which it
can be done so. A novel construction employing an auxiliary system, the bait,
which is instrumental to decoupling the system from the environment is
presented. Our approach to decoherence control in contrast to other approaches
in the literature involves the bilinear input affine model of quantum control
system which lends itself to various techniques from classical control theory,
but with non-trivial modifications to the quantum regime. The elegance of this
approach yields interesting results on open loop decouplability and Decoherence
Free Subspaces(DFS). Additionally, the feedback control of decoherence may be
related to disturbance decoupling for classical input affine systems, which
entails careful application of the methods by avoiding all the quantum
mechanical pitfalls. In the process of calculating a suitable feedback the
system has to be restructured due to its tensorial nature of interaction with
the environment, which is unique to quantum systems. The results are
qualitatively different and superior to the ones obtained via master equations.
Finally, a methodology to synthesize feedback parameters itself is given, that
technology permitting, could be implemented for practical 2-qubit systems to
perform decoherence free Quantum Computing.Comment: 17 pages, 4 Fig
Network Synthesis of Linear Dynamical Quantum Stochastic Systems
The purpose of this paper is to develop a synthesis theory for linear
dynamical quantum stochastic systems that are encountered in linear quantum
optics and in phenomenological models of linear quantum circuits. In
particular, such a theory will enable the systematic realization of
coherent/fully quantum linear stochastic controllers for quantum control,
amongst other potential applications. We show how general linear dynamical
quantum stochastic systems can be constructed by assembling an appropriate
interconnection of one degree of freedom open quantum harmonic oscillators and,
in the quantum optics setting, discuss how such a network of oscillators can be
approximately synthesized or implemented in a systematic way from some linear
and non-linear quantum optical elements. An example is also provided to
illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control
and Optimization, 200
Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback
We apply quantum filtering and control to a particle in a harmonic trap under
continuous position measurement, and show that a simple static feedback law can
be used to cool the system. The final steady state is Gaussian and dependent on
the feedback strength and coupling between the system and probe. In the limit
of weak coupling this final state becomes the ground state. An earlier model by
Haine et. al. (PRA 69, 2004) without measurement back-action showed dark
states: states that did not display error signals, thus remaining unaffected by
the control. This paper shows that for a realistic measurement process this is
not true, which indicates that a Bose-Einstein condensate may be driven towards
the ground state from any arbitrary initial state.Comment: 1 Tex, 4 PS pictures, 1 bbl fil
Empirical Determination of Bang-Bang Operations
Strong and fast "bang-bang" (BB) pulses have been recently proposed as a
means for reducing decoherence in a quantum system. So far theoretical analysis
of the BB technique relied on model Hamiltonians. Here we introduce a method
for empirically determining the set of required BB pulses, that relies on
quantum process tomography. In this manner an experimenter may tailor his or
her BB pulses to the quantum system at hand, without having to assume a model
Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum
Models and Feedback Stabilization of Open Quantum Systems
At the quantum level, feedback-loops have to take into account measurement
back-action. We present here the structure of the Markovian models including
such back-action and sketch two stabilization methods: measurement-based
feedback where an open quantum system is stabilized by a classical controller;
coherent or autonomous feedback where a quantum system is stabilized by a
quantum controller with decoherence (reservoir engineering). We begin to
explain these models and methods for the photon box experiments realized in the
group of Serge Haroche (Nobel Prize 2012). We present then these models and
methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for
the International Congress of Mathematicians in Seoul, August 13 - 21, 201
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