55 research outputs found
Limitations on quantum control
In this note we give an introduction to the topic of quantum control,
explaining what its objectives are, and describing some of its limitations.Comment: 6 page
Dissipative "Groups" and the Bloch Ball
We show that a quantum control procedure on a two-level system including
dissipation gives rise to a semi-group corresponding to the Lie algebra
semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the
action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in
the Bloch ball.Comment: 4 pages. Proceedings of Group 24, Paris, July, 200
Implementation of Quantum Gates via Optimal Control
Starting with the basic control system model often employed in NMR pulse
design, we derive more realistic control system models taking into account
effects such as off-resonant excitation for systems with fixed inter-qubit
coupling controlled by globally applied electromagnetic fields, as well as for
systems controlled by a combination of a global fields and local control
electrodes. For both models optimal control is used to find controls that
implement a set of two- and three-qubit gates with fidelity greater than
99.99%. While in some cases the optimal pulses obtained appear to be
surprisingly simple and experimentally realistic, the results also show that
the "optimal" pulses obtained in other cases are experimentally infeasible, and
more sophisticated parametrization of the control fields and numerical
algorithms are needed.Comment: 10 pages, 4 figure
Dissipative Quantum Control
Nature, in the form of dissipation, inevitably intervenes in our efforts to
control a quantum system. In this talk we show that although we cannot, in
general, compensate for dissipation by coherent control of the system, such
effects are not always counterproductive; for example, the transformation from
a thermal (mixed) state to a cold condensed (pure state) can only be achieved
by non-unitary effects such as population and phase relaxation.Comment: Contribution to Proceedings of \emph{ICCSUR 8} held in Puebla,
Mexico, July 2003, based on talk presented by Allan Solomon (ca 8 pages,
latex, 1 latex figure, 2 pdf figures converted to eps, appear to cause some
trouble
Analysis of Lyapunov Method for Control of Quantum Systems
We present a detailed analysis of the convergence properties of Lyapunov
control for finite-dimensional quantum systems based on the application of the
LaSalle invariance principle and stability analysis from dynamical systems and
control theory. For a certain class of ideal Hamiltonians, convergence results
are derived both pure-state and mixed-state control, and the effectiveness of
the method for more realistic Hamiltonians is discussed.Comment: 20 pages, 1 figure, draft versio
Experimental Hamiltonian Identification for Qubits subject to Multiple Independent Control Mechanisms
We consider a qubit subject to various independent control mechanisms and
present a general strategy to identify both the internal Hamiltonian and the
interaction Hamiltonian for each control mechanism, relying only on a single,
fixed readout process such as measurements.Comment: submitted to Proceedings of the QCMC04 (4 pages RevTeX, 5 figures
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