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 $\sigma_z$ 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

Identifying a Two-State Hamiltonian in the Presence of Decoherence

Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. For simple models of decoherence, this method can be applied even when the decoherence time is comparable to the oscillation period of the system.Comment: 8 pages, 6 figures. Minor corrections, published versio