The liouville equation in L1 spaces

AbstractWe consider the first order equation ∂u∂t=a·▽u in the Banach lattice L1(RN). By requiring a minimal amount of Sobolev regularity on the vector-field α, we show that α·▿ generates a C0-group, thereby generalizing a result of [1]. From there, we conclude the well-posedness of Liouville equation ∂u∂t= -ξ·▽xu+▽xV·ξu, for a given potential V. The comparison between the general and force-free Liouville evolution yields the existence of the wave and scattering operators, which in turn are used to prove that the spectrum of the Liouville operator is purely residual in L1(R6)

Quantum Algorithm for Continuous Global Optimization

We investigate the entwined roles of information and quantum algorithms in reducing the complexity of the global optimization problem (GOP). We show that: (1) a modest amount of additional information is sufficient to map the general continuous GOP into the (discrete) Grover problem; (2) while this additional information is actually available in some classes of GOPs, it cannot be taken advantage of within classical optimization algorithms; (3) on the contrary, quantum algorithms over a natural framework for the efficient use of this information resulting in a speed-up of the solution of the GOP

Determination of hadronic partial widths for scalar-isoscalar resonances f0(980), f0(1300), f0(1500), f_0(1750) and the broad state f0(1530^{+90}_{-250})

In the article of V.V. Anisovich et al., Yad. Fiz. 63, 1489 (2000), the K-matrix solutions for the wave IJ^{PC}=00^{++} were obtained in the mass region 450 - 1900 MeV where four resonances f0(980), f0(1300), f0(1500), f0(1750) and the broad state f0(1530^{+90}_{-250}) are located. Based on these solutions, we determine partial widths for scalar-isoscalar states decaying into the channels pi-pi, K-anti K, eta-eta, eta-eta', pi-pi-pi-pi and corresponding decay couplings.Comment: Some typos were correcte

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

Solving inverse problems of identification type by optimal control methods

Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations

Targeting qubit states using open-loop control

We present an open-loop (bang-bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman, and Milburn [Phys. Rev. A 64, #063810 (2001)] for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favorably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.Comment: 27 pages, 7 figure

Global optimization for multisensor fusion in seismic imaging

The accurate imaging of subsurface structures requires the fusion of data collected from large arrays of seismic sensors. The fusion process is formulated as an optimization problem and yields an extremely complex energy surface. Due to the very large number of local minima to be explored and escaped from, the seismic imaging problem has typically been tackled with stochastic optimization methods based on Monte Carlo techniques. Unfortunately, these algorithms are very cumbersome and computationally intensive. Here, the authors present TRUST--a novel deterministic algorithm for global optimization that they apply to seismic imaging. The excellent results demonstrate that TRUST may provide the necessary breakthrough to address major scientific and technological challenges in fields as diverse as seismic modeling, process optimization, and protein engineering

DeepNet: An Ultrafast Neural Learning Code for Seismic Imaging

A feed-forward multilayer neural net is trained to learn the correspondence between seismic data and well logs. The introduction of a virtual input layer, connected to the nominal input layer through a special nonlinear transfer function, enables ultrafast (single iteration), near-optimal training of the net using numerical algebraic techniques. A unique computer code, named DeepNet, has been developed, that has achieved, in actual field demonstrations, results unattainable to date with industry standard tools

New summing algorithm using ensemble computing

We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query complexity of the algorithm depends only on the scaling of the measurement sensitivity with the number of distinct spin sub-ensembles. From a practical point of view, the proposed algorithm may result in an exponential speedup, compared to known quantum and classical summing algorithms. However in general, this advantage exists only if the total number of function samples is below a threshold value which depends on the measurement sensitivity.Comment: 13 pages, 0 figures, VIth International Conference on Quantum Communication, Measurement and Computing (Boston, 2002

Pulse Control of Decoherence with Population Decay

The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiveness of the pulse sequences depends on a relative strength of the two decoherence processes especially when a pulse interval is slightly shorter than qubit-environment correlation times. In the short-interval limit, however, the bp sequence is always more effective than, or at least as effective as, the bb sequence.Comment: 11 pages, 7 figure