35 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
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
Subspace confinement : how good is your qubit?
The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into states outside the qubit subspace. We demonstrate how subspace leakage can be characterized using minimal theoretical assumptions by examining the Fourier spectrum of the oscillation experiment
Robust Charge-based Qubit Encoding
We propose a simple encoding of charge-based quantum dot qubits which
protects against fluctuating electric fields by charge symmetry. We analyse the
reduction of coupling to noise due to nearby charge traps and present single
qubit gates. The relative advantage of the encoding increases with lower charge
trap density.Comment: 6 Pages, 7 Figures. Published Versio