Identification of a reversible quantum gate: assessing the resources

We assess the resources needed to identify a reversible quantum gate among a finite set of alternatives, including in our analysis both deterministic and probabilistic strategies. Among the probabilistic strategies we consider unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, and we prove that parallel strategies are sufficient to unambiguously identify the unknown gate with minimum number of queries. This result is used to provide upper and lower bounds on the query complexity and on the minimum ancilla dimension. In addition, we introduce the notion of generalized t-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we give an explicit expression for the maximum probability of correct gate identification and we prove that there is no gap between the performances of deterministic strategies an those of probabilistic strategies. Hence, evaluating of the query complexity of perfect deterministic discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination. Finally, we consider discrimination strategies where the use of ancillas is forbidden, providing upper bounds on the number of additional queries needed to make up for the lack of entanglement with the ancillas.Comment: 24 + 8 pages, published versio

Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the Quantum Logic Array (QLA) architecture. Our results show that due to the exponential scaling of the computational time with the desired precision of the energy, significant amount of error correciton is required to implement the TIM problem. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.Comment: 19 pages, 8 figure

Determination of U, V, and W from single station Doppler radar radial velocities

The ST/MST (stratosphere troposphere/mesosphere stratosphere troposphere) clear air Doppler radar, or wind profiler, is an important tool in observational meteorology because of its capability to remote observe dynamic parameters of the atmosphere. There are difficulties in transforming the observed radial velocities into meteorological wind components. How this problem has been treated in the past is reviewed, and some of the analysis is recast to a form more suited to the high diagnostic abilities of a number of fixed beam configurations with reference to a linear wind field. The results, in conjunction with other works which treats problems such as the effects of finite sample volumes in the presence of nonhomogeneous atmospheric reflectivity, have implications important to the design of both individual MST/ST radars and MST/ST radar networks. The key parameters to uncoupling terms in the scaling equations are w sub x and w sub y. Whenever the stratiform condition, which states that these two parameters are negligible, is satisfied, a five beam ST radar may determine unbiased values of u, v, and w for sample volumes directly above the radar. The divergence and partial deformation of the flow may also be determined. Three beam systems can determine w and w sub z, but are unable to obtain u and v wind components uncontaminated by vertical sheer terms, even when the stratiform condition is satisfied

Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions

A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead, it is solely based on calculus, variational calculus, and linear algebra. Densities are constructed as linear combinations of scaling homogeneous terms with undetermined coefficients. The variational derivative (Euler operator) is used to compute the undetermined coefficients. The homotopy operator is used to compute the fluxes. The method is illustrated with nonlinear PDEs describing wave phenomena in fluid dynamics, plasma physics, and quantum physics. For PDEs with parameters, the method determines the conditions on the parameters so that a sequence of conserved densities might exist. The existence of a large number of conservation laws is a predictor for complete integrability. The method is algorithmic, applicable to a variety of PDEs, and can be implemented in computer algebra systems such as Mathematica, Maple, and REDUCE.Comment: To appear in: Thematic Issue on ``Mathematical Methods and Symbolic Calculation in Chemistry and Chemical Biology'' of the International Journal of Quantum Chemistry. Eds.: Michael Barnett and Frank Harris (2006

Understanding user experience of mobile video: Framework, measurement, and optimization

Since users have become the focus of product/service design in last decade, the term User eXperience (UX) has been frequently used in the field of Human-Computer-Interaction (HCI). Research on UX facilitates a better understanding of the various aspects of the user’s interaction with the product or service. Mobile video, as a new and promising service and research field, has attracted great attention. Due to the significance of UX in the success of mobile video (Jordan, 2002), many researchers have centered on this area, examining users’ expectations, motivations, requirements, and usage context. As a result, many influencing factors have been explored (Buchinger, Kriglstein, Brandt & Hlavacs, 2011; Buchinger, Kriglstein & Hlavacs, 2009). However, a general framework for specific mobile video service is lacking for structuring such a great number of factors. To measure user experience of multimedia services such as mobile video, quality of experience (QoE) has recently become a prominent concept. In contrast to the traditionally used concept quality of service (QoS), QoE not only involves objectively measuring the delivered service but also takes into account user’s needs and desires when using the service, emphasizing the user’s overall acceptability on the service. Many QoE metrics are able to estimate the user perceived quality or acceptability of mobile video, but may be not enough accurate for the overall UX prediction due to the complexity of UX. Only a few frameworks of QoE have addressed more aspects of UX for mobile multimedia applications but need be transformed into practical measures. The challenge of optimizing UX remains adaptations to the resource constrains (e.g., network conditions, mobile device capabilities, and heterogeneous usage contexts) as well as meeting complicated user requirements (e.g., usage purposes and personal preferences). In this chapter, we investigate the existing important UX frameworks, compare their similarities and discuss some important features that fit in the mobile video service. Based on the previous research, we propose a simple UX framework for mobile video application by mapping a variety of influencing factors of UX upon a typical mobile video delivery system. Each component and its factors are explored with comprehensive literature reviews. The proposed framework may benefit in user-centred design of mobile video through taking a complete consideration of UX influences and in improvement of mobile videoservice quality by adjusting the values of certain factors to produce a positive user experience. It may also facilitate relative research in the way of locating important issues to study, clarifying research scopes, and setting up proper study procedures. We then review a great deal of research on UX measurement, including QoE metrics and QoE frameworks of mobile multimedia. Finally, we discuss how to achieve an optimal quality of user experience by focusing on the issues of various aspects of UX of mobile video. In the conclusion, we suggest some open issues for future study

Design considerations for the use of laser-plasma accelerators for advanced space radiation studies

We present design considerations for the use of laser-plasma accelerators for mimicking space radiation and testing space-grade electronics. This novel application takes advantage of the inherent ability of laser-plasma accelerators to produce particle beams with exponential energy distribution, which is a characteristic shared with the hazardous relativistic electron flux present in the radiation belts of planets such as Earth, Saturn and Jupiter. Fundamental issues regarding laser-plasma interaction parameters, beam propagation, flux development, and experimental setup are discussed