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arXiv 2023年

作者： Kerger, Phillip A. Bernal Neira, David E. Izquierdo, Zoe Gonzalez Rieffel, Eleanor G. Department of Applied Mathematics and Statistics Johns Hopkins University United States Research Institute of Advanced Computer Science USRA United States Quantum Artificial Intelligence Laboratory NASA Ames Research Center United States Davidson School of Chemical Engineering Purdue University United States

The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only O(log(n)) bits of information each may be sent between processors in each round. The quantum versions of these models allow the processors instead to communicate and compute with quantum bits under the same bandwidth limitations. This leads to the following natural research question: What problems can be solved more efficiently in these quantum models than in the classical ones? Building on existing work, we contribute to this question in two ways. Firstly, we present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability;one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses Õ(n1/4) rounds of communication and Õ(n9/4) messages, where n is the number of nodes in the network. The algorithms thus achieve a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithmic frameworks with quantum subroutines. An existing framework for using a distributed version of Grover’s search algorithm to accelerate triangle finding lies at the core of the asymptotic speedup. Secondly, we carefully characterize the constants and logarithmic factors involved in our algorithms as well as related algorithms, otherwise commonly obscured by Õ notation. The analysis shows that some improvements are needed to render both our and existing related quantum and classical algorithms practical, as their asymptotic speedups only help for very large values of n. © 2023, CC BY.

关键词： Bandwidth

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Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models

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Physical Review E 2023年第6期108卷 065301-065301页

作者： Yiming Qi (岐亦铭) Lian-Ping Wang (王连平) Zhaoli Guo (郭照立) Shiyi Chen (陈十一) State Key Laboratory for Turbulence and Complex Systems College of engineering Peking University Beijing 100871 China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen Guangdong 518055 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan Hubei 430074 China Eastern Institute for Advanced Study Eastern Institute of Technology Ningbo Zhejiang 315200 China

A lifting relation connecting the distribution function explicitly with the hydrodynamic variables is necessary for the Boltzmann equation-based mesoscopic approaches in order to correctly initialize a nonuniform hydrodynamic flow. We derive two lifting relations for Guo et al.'s total-energy double-distribution-function (DDF) kinetic model [Z. L. Guo et al., Phys. Rev. E 75, 036704 (2007)], one from the Hermite expansion of the conserved and nonconserved moments, and the second from the O(τ) Chapman-Enskog (CE) approximation of the Maxwellian exponential equilibrium. While both forms are consistent to the compressible Navier-Stokes-Fourier system theoretically, we stress that the latter may introduce numerical oscillations under the recently optimized discrete velocity models [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)], namely a 27 discrete velocity model of the seventh-order Gauss-Hermite quadrature (GHQ) accuracy (D3V27A7) for the velocity field combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5) for the total energy. It is shown that the Hermite-expansion–based lifting relation can be alternatively derived from the latter approach using the truncated Hermite-polynomial equilibrium. Additionally, a relationship between the order of CE expansions and the truncated order of Hermite equilibria is developed to determine the minimal order of a Hermite equilibria required to recover any multiple-timescale macroscopic system. Next, three-dimensional compressible Taylor-Green vortex flows with different initial conditions and Ma numbers are simulated to demonstrate the effectiveness and potential issues of these lifting relations. The Hermite-expansion–based lifting relation works well in all cases, while the Chapman-Enskog-expansion–based lifting relation may produce numerical oscillations and a theoretical model is developed to predict such oscillations. Furthermore, the corresponding lifting relations for Qi et al.'s total energy

关键词： Three-dimensional turbulence Turbulence simulations Direct numerical simulations Lattice-Boltzmann methods

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MB Tools reloaded

arXiv

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arXiv 2022年

作者： Belitsky, A.V. Smirnov, A.V. Smirnov, V.A. Department of Physics Arizona State University TempeAZ85287-1504 United States Research Computing Center Moscow State University Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia Skobeltsyn Institute of Nuclear Physics Moscow State University Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia

We address the problem of evaluation of multiloop Feynman integrals by means of their Mellin-Barnes representation. After a brief overview of available capabilities though open source toolkits and their application in various circumstances, we introduce a new code MBcreate which allows one to automatically deduce a concise Mellin-Barnes representation for a given parametric integral. A thorough discussion of its implementation and use is provided. Copyright © 2022, The Authors. All rights reserved.

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Generation of highly-pure single-photon states at telecommunication wavelength

Generation of highly-pure single-photon states at telecommun...

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Frontiers in Optics, FiO 2022

作者： Kawasaki, Akito Takase, Kan Nomura, Takefumi Miki, Sigehito Terai, Hirotaka Yabuno, Masahiro China, Fumihiro Asavanant, Warit Endo, Mamoru Yoshikawa, Jun-Ichi Furusawa, Akira Department of Applied Physics School of Engineering The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Optical Quantum Computing Research Team RIKEN Center for Quantum Computing 2-1 Hirosawa Saitama Wako351-0198 Japan Advanced ICT Research Institute National Institute of Information and Communications Technology 588-2 Iwaoka Nishi-ku Hyogo Kobe651-2492 Japan Graduate School of Engineering Kobe University 1-1 Rokkodai-cho Nada-ku Hyogo Kobe657-0013 Japan

We generate highly-pure single-photon states at the telecommunication wavelength with the best record of the minimum Wigner negativity, paving the way toward the integration of universal quantum computers and construc...

ISBN: (纸本)9781557528209

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Dense Outputs from Quantum Simulations

SSRN

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SSRN 2023年

作者： Liu, Jin-Peng Lin, Lin Department of Mathematics University of California Berkeley United States Simons Institute for the Theory of Computing University of California Berkeley United States Center for Theoretical Physics Massachusetts Institute of Technology Cambridge United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley Berkeley United States

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $\epsilon$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/\epsilon)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. © 2023, The Authors. All rights reserved.

关键词： Linearization

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Charge equilibration of laser-accelerated carbon ions in a porous-structure foam target

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Physical Review A 2024年第4期109卷 042810-042810页

作者： Bubo Ma Jieru Ren Lirong Liu Wenqing Wei Benzheng Chen Shizheng Zhang Hao Xu Zhongmin Hu Fangfang Li Xing Wang Wenxuan Li Qiuyan Li Shuai Yin Jianhua Feng Xianming Zhou Yifang Gao Yuan Li Xiaohua Shi Jianxing Li Xueguang Ren Zhongfeng Xu Zhigang Deng Wei Qi Shaoyi Wang Quanping Fan Bo Cui Weiwu Wang Zongqiang Yuan Jian Teng Yuchi Wu Zhurong Cao Zongqing Zhao Yuqiu Gu Leifeng Cao Shaoping Zhu Rui Cheng Yu Lei Zhao Wang Zexian Zhou Guoqing Xiao Hongwei Zhao Dieter H. H. Hoffmann Weimin Zhou Yongtao Zhao MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter School of Science Xi'an Jiaotong University Xi'an 710049 China Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center China Academy of Engineering Physics Mianyang 621900 China Advanced Materials Testing Technology Research Center Shenzhen University of Technology Shenzhen 518118 China Institute of Applied Physics and Computational Mathematics Beijing 100094 China Graduate School China Academy of Engineering Physics Beijing 100088 China Institute of Modern Physics Chinese Academy of Sciences Lanzhou 710049 China

The equilibrium charge state distribution of laser-accelerated carbon ions traversing a tri-cellulose-acetate (TCA, C9H16O8) foam target was measured experimentally. The ions were generated through the target normal sheath acceleration mechanism. This allowed us to obtain the equilibrium charge state for a wide energy range near the maximum energy loss within a single laser shot. The foam had a porous structure with 2 mg/cm3 volume density, which is between the typical density of gas- and solid-state matter. We found that the measured average equilibrium charge states were significantly underestimated by theoretical models applicable for gas targets, while were in close agreement with both semiempirical formulas and rate equation predictions based on ion-solid interactions. The solid-density fiber filaments in the current foam structure were attributed and demonstrated. The target density effects, which increase the ionization probability through frequent collisions and decrease the electron capture probability, were proven to play an important role in the foam target. Since the foam targets are widely used in laser plasma interaction experiments, our findings are relevant for a broad range of applications.

关键词： Atomic & molecular collisions Beam dynamics Beam injection, extraction & transport Lasers Ions Low- & intermediate-energy accelerators Atomic Properties Ab initio molecular dynamics Bragg spectroscopy Inner-shell processes

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Dense outputs from quantum simulations

arXiv

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arXiv 2023年

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time T and error tolerance ǫ. Our results demonstrate that the linearization approach can nearly achieve optimal complexity O(T/ǫ) for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. Copyright © 2023, The Authors. All rights reserved.

关键词： Linearization

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Non-Gaussian-state generation with time-gated photon detection

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Physical Review research 2023年第3期5卷 033156-033156页

作者： Tatsuki Sonoyama Kazuma Takahashi Baramee Charoensombutamon Sachiko Takasu Kaori Hattori Daiji Fukuda Kosuke Fukui Kan Takase Warit Asavanant Jun-ichi Yoshikawa Mamoru Endo Akira Furusawa Department of Applied Physics School of Engineering The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan National Institute of Advanced Industrial Science and Technology Tsukuba Ibaraki 305-8563 Japan AIST-UTokyo Advanced Operando-Measurement Technology Open Innovation Laboratory Tsukuba Ibaraki 305-8563 Japan Optical Quantum Computing Research Team RIKEN Center for Quantum Computing 2-1 Hirosawa Wako Saitama 351-0198 Japan

Non-Gaussian states of light, which are essential in fault-tolerant and universal optical quantum computation, are typically generated by a heralding scheme using photon detectors. Recently, it has been theoretically shown that the large timing jitter of the photon detectors deteriorates the purity of the generated non-Gaussian states [T. Sonoyama et al., Phys. Rev. A 105, 043714 (2022)]. Here, we circumvent this problem by time-gated photon detection and generate non-Gaussian states with Wigner negativity using continuous-wave light. We use a fast optical switch for time gating to effectively improve the timing jitter of a photon-number-resolving detector based on a transition edge sensor from 50 ns to 10 ns. As a result, we generate non-Gaussian states with Wigner negativity of −0.011±0.004 (ℏ=1), which cannot be observed without the time-gated photon detection method. These results confirm the effect of the timing jitter on non-Gaussian state generation experimentally for the first time. The proposed time-gated photon detection method would be useful for high-purity non-Gaussian state preparation in optical quantum information processing.

关键词： Quantum optics Quantum state engineering Quantum states of light Single-photon detectors

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Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation

arXiv

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arXiv 2024年

作者： An, Dong Childs, Andrew M. Lin, Lin Ying, Lexing Beijing International Center for Mathematical Research Peking University China Joint Center for Quantum Information and Computer Science University of Maryland College Park United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Mathematics University of California Berkeley United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley United States Department of Mathematics Stanford University United States Institute for Computational and Mathematical Engineering Stanford University United States

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for non-normal matrices. We propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation (LCHS) method [An, Liu, Lin, Phys. Rev. Lett. 131, 150603, 2023;An, Childs, Lin, arXiv:2312.03916] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, A-k, and the exponential of the matrix inverse, e-A-1. The latter can be interpreted as the solution of a mass-matrix differential equation of the form Au′(t) = -u(t). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting A, reducing the computational complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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A Stochastic Flight Problem Simulation to Minimize Cost of Refuelling

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Computers, Materials & Continua 2021年第10期69卷 849-871页

作者： Said Ali Hassan Khalid Alnowibet Miral H.Khodeir Prachi Agrawal Adel F.Alrasheedi Ali Wagdy Mohamed Department of Operations Research and Decision Support Faculty of Computers and Artificial IntelligenceCairo UniversityGiza12613Egypt Department of Statistics and Operations Research College of ScienceKing Saud UniversityRiyadh11451Kingdom of Saudi Arabia Department of Mathematics and Scientific Computing National Institute of Technology HamirpurHimachal Pradesh177005India Department of Operations Research Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGizaEgypt

Commercial airline companies are continuously seeking to implement strategies for minimizing costs of fuel for their flight routes as acquiring jet fuel represents a significant part of operating and managing expenses for airline activities.A nonlinear mixed binary mathematical programming model for the airline fuel task is presented to minimize the total cost of refueling in an entire flight route *** model is enhanced to include possible discounts in fuel prices,which are performed by adding dummy variables and some restrictive constraints,or by fitting a suitable distribution function that relates prices to purchased *** obtained fuel plan explains exactly the amounts of fuel in gallons to be purchased from each airport considering tankering strategy while minimizing the pertinent cost of the whole flight *** relation between the amount of extra burnt fuel taken through tinkering strategy and the total flight time is also considered.A case study is introduced for a certain flight rotation in domestic US air transport *** mathematical model including stepped discounted fuel prices is *** problem has a stochastic nature as the total flight time is a random variable,the stochastic nature of the problem is realistic and more appropriate than the deterministic *** stochastic style of the problem is simulated by introducing a suitable probability distribution for the flight time duration and generating enough number of runs to mimic the probabilistic real *** similar real application problems are modelled as nonlinear mixed binary ones that are difficult to handle by exact ***,metaheuristic approaches are widely used in treating such different optimization *** this paper,a gaining sharing knowledge-based procedure is used to handle the mathematical *** algorithm basically based on the process of gaining and sharing knowledge throughout the human *** generated simulation runs of

关键词： Stochastic flight problem cost of refuelling ferrying strategy tankering discounted prices simulation procedure nonlinear mixed binary model metaheuristic algorithm gaining-sharing knowledge-based algorithm

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