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arXiv 2020年

作者： Hashim, Akel Naik, Ravi K. Morvan, Alexis Ville, Jean-Loup Mitchell, Bradley Kreikebaum, John Mark Davis, Marc Smith, Ethan Iancu, Costin O'Brien, Kevin P. Hincks, Ian Wallman, Joel J. Emerson, Joseph Siddiqi, Irfan Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Graduate Group in Applied Science and Technology University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada Institute for Quantum Computing and Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors, and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally-measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing. Copyright © 2020, The Authors. All rights reserved.

关键词： Benchmarking

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Quantum Simulation for High-Energy Physics

引用

PRX Quantum 2023年第2期4卷 027001-027001页

作者： Christian W. Bauer Zohreh Davoudi A. Baha Balantekin Tanmoy Bhattacharya Marcela Carena Wibe A. de Jong Patrick Draper Aida El-Khadra Nate Gemelke Masanori Hanada Dmitri Kharzeev Henry Lamm Ying-Ying Li Junyu Liu Mikhail Lukin Yannick Meurice Christopher Monroe Benjamin Nachman Guido Pagano John Preskill Enrico Rinaldi Alessandro Roggero David I. Santiago Martin J. Savage Irfan Siddiqi George Siopsis David Van Zanten Nathan Wiebe Yukari Yamauchi Kübra Yeter-Aydeniz Silvia Zorzetti Physics Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics Maryland Center for Fundamental Physics and the NSF Institute for Robust Quantum Simulation University of Maryland College Park Maryland 20742 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA T-2 Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Enrico Fermi Institute University of Chicago Chicago Illinois 60637 USA Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Department of Physics University of Chicago Chicago Illinois 60637 USA Department of Physics and Illinois Center for the Advanced Study of the Universe and Illinois Quantum Information Science and Technology Center University of Illinois Urbana Illinois 61801 USA QuEra Computing Inc Boston Massachusetts 02135 USA Department of Mathematics University of Surrey Guildford Surrey GU2 7XH United Kingdom Center for Nuclear Theory Department of Physics and Astronomy Stony Brook University New York 11794-3800 USA Department of Physics Brookhaven National Laboratory Upton New York 11973 USA Peng Huanwu Center for Fundamental Theory Hefei Anhui 230026 China Interdisciplinary Center for Theoretical Study University of Science and Technology of China Hefei Anhui 230026 China Pritzker School of Molecular Engineering Chicago Quantum Exchange and Kadanoff Center for Theoretical Physics University of Chicago Illinois 60637 USA qBraid Co. Harper Court 5235 Chicago Illinois 60615 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA Department of Physics and Astronomy University of Iowa Iowa City Iowa 52242 USA Duke Quantum Center Duke University Durham North Carolina 27701 USA Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Department of Physics Duke University

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

关键词： Quantum simulation

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Data-driven polynomial chaos expansions: A weighted least-square approximation

arXiv

引用

arXiv 2018年

作者： Guo, Ling Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments of the input random variables to develop an arbitrary polynomial chaos expansion, and then use such data-driven bases to perform UQ computations. Here we adopt the bases construction procedure by following [1], where the bases are computed by using matrix operations on the Hankel matrix of moments. Different from previous works, in the postprocessing part, we propose a weighted least-squares approach to solve UQ problems. This approach includes a sampling strategy and a least-squares solver. The main features of our approach are two folds: On one hand, our sampling strategy is independent of the random input. More precisely, we propose to sampling with the equilibrium measure, and this measure is also independent of the data-driven bases. Thus, this procedure can be done in prior (or in a off- line manner). On the other hand, we propose to solve a Christoffel function weighted least-square problem, and this strategy is quasi-linearly stable - the required number of PDE solvers depends linearly (up to a logarithmic factor) on the number of (data-driven) bases. This new approach is thus promising in dealing with a class of problems with epistemic uncertainties. Several numerical tests are presented to show the effectiveness of our approach. Copyright © 2018, The Authors. All rights reserved.

关键词： Uncertainty analysis

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ChebNet: Efficient and Stable Constructions of Deep Neural Networks with Rectified Power Units via Chebyshev Approximation

arXiv

引用

arXiv 2019年

作者： Tang, Shanshan Li, Bo Yu, Haijun Software Development Center Industrial and Commercial Bank of China No. 16 Building of ZhongGuanCun Software Park Haidian District Beijing100193 China Huawei Technologies Co. Ltd Bai Ruida Apartment Bantian Street Longgang District Shenzhen518129 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In a previous study [B. Li, S. Tang and H. Yu, Commun. Comput. Phy. 27(2):379-411, 2020], it is shown that deep neural networks built with rectified power units (RePU) as activation functions can give better approximation for sufficient smooth functions than those built with rectified linear units, by converting polynomial approximations using power series into deep neural networks with optimal complexity and no approximation error. However, in practice, power series approximations are not easy to obtain due to the associated stability issue. In this paper, we propose a new and more stable way to construct RePU deep neural networks based on Chebyshev polynomial approximations. By using a hierarchical structure of Chebyshev polynomial approximation in frequency domain, we obtain efficient and stable deep neural network construction, which we call ChebNet. The approximation of smooth functions by ChebNets is no worse than the approximation by deep RePU nets using power series. On the same time, ChebNets are much more stable. Numerical results show that the constructed ChebNets can be further fine-tuned to obtain much better results than those obtained by tuning deep RePU nets constructed by power series approach. As spectral accuracy is hard to obtain by direct training of deep neural networks, ChebNets provide a practical way to obtain spectral accuracy, it is expected to be useful in real applications that require efficient approximations of smooth functions. © 2019, CC BY-NC-ND.

关键词： Chebyshev polynomials

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Capacity optimality of AMP in coded systems

arXiv

引用

arXiv 2019年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Hong Kong SAR China Nomi 923-1292 Japan Department of Electrical Engineering City University of Hong Kong Hong Kong SAR China Algorithm Department ZTE Corporation Shenzhen 518057 China State Key Laboratory of Mobile Network Mobile Multimedia Technology ZTE Corporation Shenzhen 518057 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Science Beijing China Department of Electronic Engineering City University of Hong Kong Hong Kong SAR China

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. © 2019, CC BY-NC-SA.

关键词： Message passing

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A lowest-order mixed finite element method for the elastic transmission eigenvalue problem

arXiv

引用

arXiv 2018年

作者： Xi, Yingxia Ji, Xia School of Science Nanjing University of Science and Technology Nanjing210094 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

The goal of this paper is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. The problem is challenging since it is nonlinear, non-self-adjoint, and of fourth order. In this paper, we construct a lowest-order mixed finite element method which is close to the Ciarlet-Raviart mixed finite element method. This scheme is based on Lagrange finite elements and is one of the less expensive methods in terms of the amount of degrees of freedom. Due to the non-self-adjointness, the discretization of elastic transmission eigenvalue problem leads to a non-classical mixed method which does not fit into the framework of classical theoretical analysis. In stead, we obtain the convergence analysis based on the spectral approximation theory of compact operators. Numerical examples are presented to verify the theory. Both real and complex eigenvalues can be *** Codes 65N25, 65N30, 47B07 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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AbdomenCT-1K: Is abdominal organ segmentation a solved problem?

arXiv

引用

arXiv 2020年

作者： Ma, Jun Zhang, Yao Gu, Song Zhu, Cheng Ge, Cheng Zhang, Yichi An, Xingle Wang, Congcong Wang, Qiyuan Liu, Xin Cao, Shucheng Zhang, Qi Liu, Shangqing Wang, Yunpeng Li, Yuhui He, Jian Yang, Xiaoping Department of Mathematics Nanjing University of Science and Technology China Institute of Computing Technology Chinese Academy of Sciences University of Chinese Academy of Sciences China AI Lab Lenovo Research School of Automation Nanjing University of Information Science and Technology China Shenzhen Haichuang Medical CO. LTD. China Institute of Bioinformatics and Medical Engineering Jiangsu University of Technology China School of Biological Science and Medical Engineering Beihang University China Beijing Infervision Technology CO. LTD. China School of Computer Science and Engineering Tianjin University of Technology China Department of Computer Science Norwegian University of Science and Technology Norway School of Electronic Science and Engineering Nanjing University China Suzhou LungCare Medical Technology Co. Ltd China Bioengineering Biological and Environmental Science and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Computer and Information Science Faculty of Science and Technology University of Macau China School of Biomedical Engineering Southern Medical University China Institutes of Biomedical Sciences Fudan University China Computational Biology University of Southern California United States Department of Radiology Nanjing Drum Tower Hospital The Affiliated Hospital Nanjing University Medical School China Department of Mathematics Nanjing University China

With the unprecedented developments in deep learning, automatic segmentation of main abdominal organs seems to be a solved problem as state-of-the-art (SOTA) methods have achieved comparable results with inter-rater variability on many benchmark datasets. However, most of the existing abdominal datasets only contain single-center, single-phase, single-vendor, or single-disease cases, and it is unclear whether the excellent performance can generalize on diverse datasets. This paper presents a large and diverse abdominal CT organ segmentation dataset, termed AbdomenCT-1K, with more than 1000 (1K) CT scans from 12 medical centers, including multi-phase, multi-vendor, and multi-disease cases. Furthermore, we conduct a large-scale study for liver, kidney, spleen, and pancreas segmentation and reveal the unsolved segmentation problems of the SOTA methods, such as the limited generalization ability on distinct medical centers, phases, and unseen diseases. To advance the unsolved problems, we further build four organ segmentation benchmarks for fully supervised, semi-supervised, weakly supervised, and continual learning, which are currently challenging and active research topics. Accordingly, we develop a simple and effective method for each benchmark, which can be used as out-of-the-box methods and strong baselines. We believe the AbdomenCT-1K dataset will promote future in-depth research towards clinical applicable abdominal organ segmentation methods. © 2020, CC BY-NC-SA.

关键词： Computerized tomography

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On the perturbation of an L2-orthogonal projection

arXiv

引用

arXiv 2018年

作者： Xu, Xuefeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

The L2-orthogonal projection is an important mathematical tool in scientific computing and numerical analysis, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized algorithms. In some numerical applications, the entries of a matrix will seldom be known exactly, so it is necessary to develop some bounds to characterize the effects of the uncertainties caused by matrix perturbation. In this paper, we establish new perturbation bounds for the L2orthogonal projection onto the column space of a matrix, which involve upper (lower) bounds and combined upper (lower) bounds. The new results contain some sharper counterparts of the existing bounds. Numerical examples are also given to illustrate our theoretical results.15A09, 15A18, 47A55, 65F35 Copyright © 2018, The Authors. All rights reserved.

关键词： Singular value decomposition

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On the perturbation of the Moore–Penrose inverse of a matrix

arXiv

引用

arXiv 2018年

Over the past decades, the Moore–Penrose inverse has been extensively investigated and widely applied in many fields. One reason for this interest is that the Moore–Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. However, the entries of a matrix will seldom be known exactly in numerical applications, so it is necessary to develop some bounds to characterize the effects of matrix perturbation. In this paper, we establish new perturbation bounds for the Moore–Penrose inverse of a matrix, which include some sharper counterparts of the existing upper bounds. Numerical examples are also provided to illustrate our theoretical results. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse problems

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STABILITY ANALYSIS FOR NONLINEAR SCHRODINGER EQUATIONS WITH NONLINEAR ABSORBING BOUNDARY CONDITIONS

引用

Journal of computational mathematics 2017年第1期35卷 1-18页

作者： Jiwei Zhang Zhenli Xu Xiaonan Wu Desheng Wang Applied and Computational Mathematics Division Beijing Computational Science Research Center China Department of Mathematics Institute of Natural Sciences and MOE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore

Local absorbing boundary conditions （LABCs） for nonlinear Schr6dinger equations have been constructed in papers [PRE 78（2008） 026709; and PRE 79 （2009） 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the re- duced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demon- strate the effectiveness of our boundary conditions and validate the theoretical analysis.

关键词： Nonlinear SchrSdinger equations Energy estimates Absorbing boundaryconditions.

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