1,024 research outputs found

    Percolation, renormalization, and quantum computing with non-deterministic gates

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    We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of non-deterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.Comment: 5 pages, 4 figures, discussion of strategies to deal with further imperfections extended, references update

    Weak limits for quantum random walks

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    We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With XnX_n denoting position at time nn, we show that Xn/nX_n/n converges weakly as nn \to \infty to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods

    Robust nonparametric detection of objects in noisy images

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    We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd

    Dynamical Exchanges in Facilitated Models of Supercooled liquids

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    We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions d=1d=1, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related, and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, c2 \sim c^{-2}, with cc being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings.Comment: 11 pages, 14 figures, minor corrections made, paper published in Journal of Chemical Physic

    Ovarian and cervical cancer awareness: development of two validated measurement tools.

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    The aim of the study was to develop and validate measures of awareness of symptoms and risk factors for ovarian and cervical cancer (Ovarian and Cervical Cancer Awareness Measures)
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