The Experts below are selected from a list of 199716 Experts worldwide ranked by ideXlab platform
Roberto Osellame - One of the best experts on this subject based on the ideXlab platform.
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learning an unknown transformation via a genetic approach
Scientific Reports, 2017Co-Authors: Nicolo Spagnolo, Andrea Crespi, Roberto Osellame, Roberta Ramponi, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Marco BentivegnaAbstract:Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson Sampling Problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.
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integrated multimode interferometers with arbitrary designs for photonic boson Sampling
Nature Photonics, 2013Co-Authors: Andrea Crespi, Roberto Osellame, Roberta Ramponi, Daniel J Brod, Ernesto F Galvao, Nicolo Spagnolo, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Fabio SciarrinoAbstract:The boson-Sampling Problem was demonstrated by studying three-photon interference in a five-mode integrated interferometer containing three-dimensional S-bent waveguides. Three single photons were input into the interferometer and the probability ratios of all events were measured. The results agree with quantum mechanical predictions for three-photon interference.
Karlheinz Gröchenig - One of the best experts on this subject based on the ideXlab platform.
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Multivariate Gabor frames and Sampling of entire functions of several variables
Applied and Computational Harmonic Analysis, 2011Co-Authors: Karlheinz GröchenigAbstract:Abstract We investigate Gabor frames with Gaussian windows in higher dimensions. This Problem is equivalent to a Sampling Problem in Bargmann–Fock space. In contrast to dimension d = 1 , the frame property is no longer characterized by the density of the lattice. We give sufficient conditions for complex lattices to generate a multivariate Gabor frame with a Gaussian window.
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NON-UNIFORM Sampling IN SHIFT-INVARIANT SPACES
2007Co-Authors: Akram Aldroubi, Karlheinz GröchenigAbstract:This article discusses modern techniques for non-uniform Sampling and reconstruction of functions in shift-invariant spaces. The reconstruction of a function or signal or image f from its non-uniform samples f(xj) is a common task in many applications in data or signal or image processing. The non-uniformity of the Sampling set is often a fact of life and prevents the use of the standard methods from Fourier analysis. The non-uniform Sampling Problem is usually treated in the context of band-limited functions and with tools from complex analysis. However, many applied Problems impose different a priori constraints on the type of function. These constraints are taken into consideration by investigating the Problem in general shift-invariant spaces rather than for band-limited functions only. This generalization requires a new set of techniques and ideas. While some of the tools are implicitly used in certain questions in approximation theory, wavelet theory and frame theory, they have received little attention in the context of Sampling theory, and thus some of the current literature seems unnecessarily complicated. This article is a survey as well as a research paper and is intended to provide the main building blocks for a general theory of non-uniform Sampling in shift-invariant spaces. Emphasis is on the following features: (a) Within the setting of shift-invariant spaces the Sampling Problem is well-defined; (b) The general theory works in arbitrary dimension and for a broad class of generators; (c) For any sufficiently dense non-uniform Sampling set useful iterative reconstruction algorithms are derived; (d) In order to model the decay conditions encountered in natural signals and images, the Sampling theory is developed in weighted L-spaces. This is a useful innovation over the standard L techniques. Date: January 23, 2000. 1991 Mathematics Subject Classification. Primary 41A15,42C15, 46A35, 46E15, 46N99, 47B37.
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RECONSTRUCTION ALGORITHMS IN IRREGULAR Sampling
Mathematics of Computation, 1992Co-Authors: Karlheinz GröchenigAbstract:A constructive solution of the irregular Sampling Problem for band- limited functions is given. We show how a band-limited function can be com- pletely reconstructed from any random Sampling set whose density is higher than the Nyquist rate, and give precise estimates for the speed of convergence of this iteration method. Variations of this algorithm allow for irregular Sampling with derivatives, reconstruction of band-limited functions from local averages, and irregular Sampling of multivariate band-limited functions. In the irregular Sampling Problem one is asked whether and how a band- limited function / can be completely reconstructed from its irregularly sam- pled values f(xi). This has many applications in signal and image processing, seismology, meteorology, medical imaging, etc. Finding constructive solutions of this Problem has received considerable attention among mathematicians and engineers. The mathematical literature provides several uniqueness results (1, 2, 17, 18, 19). It is now part of the folklore that for stable Sampling the Sampling rate must be at least the Nyquist rate (18). These results, as deep as they are, have had little impact for the applied sciences, because they were not constructive. If the Sampling set is just a perturbation of the regular overSampling, then a reconstruction method has been obtained in a seminal paper by Duffin and Schaeffer (6) (see also (29)): if for some L > 0, a > 0, and o > 0 the Sampling points xk , k e Z , satisfy (a) \xk - ok\ a, k ^ I, then the norm equivalence A iR \f(x)\2dx ) with w < n/o. This norm equivalence implies that it is possible to reconstruct / through an iterative procedure, the so-called frame method. Most of the later work on constructive methods consists of variations of this method (3, 21, 22, 26). The above conditions on the Sampling set exclude random irregular Sampling sets, e.g., sets with regions of higher Sampling density. A partial, but undesirable remedy, to handle highly irregular Sampling sets, would be to force the above conditions by throwing away information on part of the points and accept a very slow convergence of the iteration.
Roberta Ramponi - One of the best experts on this subject based on the ideXlab platform.
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learning an unknown transformation via a genetic approach
Scientific Reports, 2017Co-Authors: Nicolo Spagnolo, Andrea Crespi, Roberto Osellame, Roberta Ramponi, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Marco BentivegnaAbstract:Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson Sampling Problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.
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integrated multimode interferometers with arbitrary designs for photonic boson Sampling
Nature Photonics, 2013Co-Authors: Andrea Crespi, Roberto Osellame, Roberta Ramponi, Daniel J Brod, Ernesto F Galvao, Nicolo Spagnolo, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Fabio SciarrinoAbstract:The boson-Sampling Problem was demonstrated by studying three-photon interference in a five-mode integrated interferometer containing three-dimensional S-bent waveguides. Three single photons were input into the interferometer and the probability ratios of all events were measured. The results agree with quantum mechanical predictions for three-photon interference.
Michael C Fu - One of the best experts on this subject based on the ideXlab platform.
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simulation in financial engineering importance Sampling in derivative securities pricing
Winter Simulation Conference, 2000Co-Authors: Yi Su, Michael C FuAbstract:We formulate the importance Sampling Problem as a parametric minimization Problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn't depend on the form of payoff functions and differentiability of the sample path, and thus is more universally applicable and computationally efficient. Under suitable conditions, the objective function is a convex function, the IPA estimator presented is unbiased, and the corresponding stochastic approximation algorithm converges to the true optimal value.
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Winter Simulation Conference - Simulation in financial engineering: importance Sampling in derivative securities pricing
2000Co-Authors: Yi Su, Michael C FuAbstract:We formulate the importance Sampling Problem as a parametric minimization Problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn't depend on the form of payoff functions and differentiability of the sample path, and thus is more universally applicable and computationally efficient. Under suitable conditions, the objective function is a convex function, the IPA estimator presented is unbiased, and the corresponding stochastic approximation algorithm converges to the true optimal value.
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importance Sampling in derivative securities pricing
Winter Simulation Conference, 2000Co-Authors: Yi Su, Michael C FuAbstract:We formulate the importance Sampling Problem as a parametric minimization Problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn't depend on the form of payoff functions and differentiability of the sample path, and thus is more universally applicable and computationally efficient. Under suitable conditions, the objective function is a convex function, the IPA estimator presented is unbiased, and the corresponding stochastic approximation algorithm converges to the true optimal value.
Andrea Crespi - One of the best experts on this subject based on the ideXlab platform.
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learning an unknown transformation via a genetic approach
Scientific Reports, 2017Co-Authors: Nicolo Spagnolo, Andrea Crespi, Roberto Osellame, Roberta Ramponi, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Marco BentivegnaAbstract:Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson Sampling Problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.
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integrated multimode interferometers with arbitrary designs for photonic boson Sampling
Nature Photonics, 2013Co-Authors: Andrea Crespi, Roberto Osellame, Roberta Ramponi, Daniel J Brod, Ernesto F Galvao, Nicolo Spagnolo, Chiara Vitelli, Enrico Maiorino, Paolo Mataloni, Fabio SciarrinoAbstract:The boson-Sampling Problem was demonstrated by studying three-photon interference in a five-mode integrated interferometer containing three-dimensional S-bent waveguides. Three single photons were input into the interferometer and the probability ratios of all events were measured. The results agree with quantum mechanical predictions for three-photon interference.
