9,722 research outputs found
Selective and Efficient Quantum Process Tomography
In this paper we describe in detail and generalize a method for quantum
process tomography that was presented in [A. Bendersky, F. Pastawski, J. P.
Paz, Physical Review Letters 100, 190403 (2008)]. The method enables the
efficient estimation of any element of the --matrix of a quantum process.
Such elements are estimated as averages over experimental outcomes with a
precision that is fixed by the number of repetitions of the experiment.
Resources required to implement it scale polynomically with the number of
qubits of the system. The estimation of all diagonal elements of the
--matrix can be efficiently done without any ancillary qubits. In turn,
the estimation of all the off-diagonal elements requires an extra clean qubit.
The key ideas of the method, that is based on efficient estimation by random
sampling over a set of states forming a 2--design, are described in detail.
Efficient methods for preparing and detecting such states are explicitly shown.Comment: 9 pages, 5 figure
Approximate F_2-Sketching of Valuation Functions
We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function f : F_2^n - > R with small expected squared error. We develop a general theory of linear sketching for such functions through which we analyze their dimension for most commonly studied types of valuation functions: additive, budget-additive, coverage, alpha-Lipschitz submodular and matroid rank functions. This gives a characterization of how many bits of information have to be stored about the input x so that one can compute f under additive updates to its coordinates.
Our results are tight in most cases and we also give extensions to the distributional version of the problem where the input x in F_2^n is generated uniformly at random. Using known connections with dynamic streaming algorithms, both upper and lower bounds on dimension obtained in our work extend to the space complexity of algorithms evaluating f(x) under long sequences of additive updates to the input x presented as a stream. Similar results hold for simultaneous communication in a distributed setting
Fully Complex Magnetoencephalography
Complex numbers appear naturally in biology whenever a system can be analyzed
in the frequency domain, such as physiological data from magnetoencephalography
(MEG). For example, the MEG steady state response to a modulated auditory
stimulus generates a complex magnetic field for each MEG channel, equal to the
Fourier transform at the stimulus modulation frequency. The complex nature of
these data sets, often not taken advantage of, is fully exploited here with new
methods. Whole-head, complex magnetic data can be used to estimate complex
neural current sources, and standard methods of source estimation naturally
generalize for complex sources. We show that a general complex neural vector
source is described by its location, magnitude, and direction, but also by a
phase and by an additional perpendicular component. We give natural
interpretations of all the parameters for the complex equivalent-current dipole
by linking them to the underlying neurophysiology. We demonstrate complex
magnetic fields, and their equivalent fully complex current sources, with both
simulations and experimental data.Comment: 23 pages, 1 table, 5 figures; to appear in Journal of Neuroscience
Method
Techniques for augmenting the visualisation of dynamic raster surfaces
Despite their aesthetic appeal and condensed nature, dynamic raster surface representations such as a temporal series of a landform and an attribute series of a socio-economic attribute of an area, are often criticised for the lack of an effective information delivery and interactivity.In this work, we readdress some of the earlier raised reasons for these limitations -information-laden quality of surface datasets, lack of spatial and temporal continuity in the original data, and a limited scope for a real-time interactivity. We demonstrate with examples that the use of four techniques namely the re-expression of the surfaces as a framework of morphometric features, spatial generalisation, morphing, graphic lag and brushing can augment the visualisation of dynamic raster surfaces in temporal and attribute series
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