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Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

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Science China(Physics,Mechanics & Astronomy) 2019年第6期62卷 13-20页

作者： Tao Xin Liang Hao Shi-Yao Hou Guan-Ru Feng Gui-Lu Long State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics Tsinghua University Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Center for Quantum Computing Peng Cheng Laboratory Shenzhen Key Laboratory of Quantum Science and Engineering Southern University of Science and Technology Institute of Applied Physics and Computational Mathematics Center for Computational Sciences Sichuan Normal University College of Physics and Electronic Engineering Sichuan Normal University Institute for Quantum Computing Waterloo Tsinghua National Laboratory of Information Science and Technology The Innovative Center of Quantum Matter

Quantum state preparation plays an equally important role as quantum operations and measurements in quantum information processing. The previous methods for initialization require either an exponential number of experiments, or cause signal reduction or place restrictions on molecular structures. In this study, we propose three types of quantum circuits for preparing the pseudo-pure states of(n-1) qubits in the n-coupled Hilbert space, which simply needs the assistance of one ancilla spin and two different experiments independent of n. Most importantly, our methods work well on homo-nuclear and hetero-nuclear molecules without the reduction of signals in the gradient field. As a proof-of-principle demonstration, we experimentally prepared the pseudo-pure states of heteronuclear 2-qubit and homonuclear 4-qubit molecules using a nuclear magnetic resonance quantum information processor.

关键词： quantum state preparation nuclear magnetic resonance quantum algorithms

Measuring spin precession from massive black hole binaries with gravitational waves: insights from time-domain signal morphology

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arXiv 2025年

作者： Miller, Simona J. Isi, Maximiliano Chatziioannou, Katerina Varma, Vijay Hourihane, Sophie TAPIR California Institute of Technology PasadenaCA91125 United States LIGO Laboratory California Institute of Technology PasadenaCA91125 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States

Robustly measuring binary black hole spins via gravitational waves is key to understanding these systems’ astrophysical origins, but remains challenging—especially for high-mass systems, whose signals are short and dominated by the merger. Nonetheless, events like GW190521 show that strong spin precession can indeed be gleaned from high-mass systems. In this work, we track how spin precession imprints on simulated high-mass binary black hole signals cycle-by-cycle using time-domain inference. We investigate a suite of signals, all with the same spins and (near-unity) mass ratio—yielding identical spin evolution—but different signal-to-noise ratios, total masses, and extrinsic angles, which affect the observed waveform morphology. We truncate each signal at various times and infer source parameters using only the data before or after each cutoff. The resultant posterior allows us to identify which time segments of each signal inform its spin precession constraints. We find that at a sufficiently high post-peak signal-to-noise ratio (SNR, ρ ∼ 20), spin precession can be constrained by the NRSur7dq4 waveform model when just the post-peak data (i.e., ringdown) is visible. Similarly, at a large enough pre-cutoff SNR (ρ ∼ 10), spin precession can be constrained using only pre-peak data (i.e., inspiral);this occurs for signals with detector-frame total mass 100M☉ at GW190521’s SNR. Finally, we vary the inclination, polarization, and phase angles, finding that their configuration need not be fine-tuned to measure spin precession, even for very high-mass and short signals with 2-3 observable cycles. We do not find that the same morphological features consistently drive precession constraints: in some signals, precession inference hinges on the relationship between a loud merger and quiet pre-merger cycle, as was the case for GW190521, but this is not generically true. Our studies enable a morphological understanding of precession that can help bolster confidence in precessio

关键词： Gravitational effects

cuFINUFFT: A load-balanced GPU library for general-purpose nonuniform FFTs

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arXiv 2021年

作者： Shih, Yu-Hsuan Wright, Garrett Andén, Joakim Blaschke, Johannes Barnett, Alex H. Courant Institute of Mathematical Sciences New York University New YorkNY United States PACM Princeton University PrincetonNJ United States Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Center for Computational Mathematics Flatiron Institute New YorkNY United States

Nonuniform fast Fourier transforms dominate the computational cost in many applications including image reconstruction and signal processing. We thus present a general-purpose GPU-based CUDA library for type 1 (nonuniform to uniform) and type 2 (uniform to nonuniform) transforms in dimensions 2 and 3, in single or double precision. It achieves high performance for a given user-requested accuracy, regardless of the distribution of nonuniform points, via cache-aware point reordering, and load-balanced blocked spreading in shared memory. At low accuracies, this gives on-GPU throughputs around 109 nonuniform points per second, and (even including host-device transfer) is typically 4-10× faster than the latest parallel CPU code FINUFFT (at 28 threads). It is competitive with two established GPU codes, being up to 90× faster at high accuracy and/or type 1 clustered point distributions. Finally we demonstrate a 5-12× speedup versus CPU in an X-ray diffraction 3D iterative reconstruction task at 10−12 accuracy, observing excellent multi-GPU weak scaling up to one rank per GPU. Copyright © 2021, The Authors. All rights reserved.

关键词： Graphics processing unit

Survey of physics reasoning on uncertainty concepts in experiments: an assessment of measurement uncertainty for introductory physics labs

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arXiv 2023年

作者： Vignal, Michael Geschwind, Gayle Pollard, Benjamin Henderson, Rachel Caballero, Marcos D. Lewandowski, H.J. JILA National Institute of Standards and Technology The University of Colorado BoulderCO80309 United States Department of Physics University of Colorado 390 UCB BoulderCO80309 United States Department of Physics Worcester Polytechnic Institute 100 Institute Road WorcesterMA01609 United States Department of Physics & Astronomy CREATE for STEM Institute Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science & Engineering Michigan State University East LansingMI48824 United States Department of Physics Center for Computing in Science Education University of Oslo Oslo0315 Norway

Measurement uncertainty is a critical feature of experimental research in the physical sciences, and the concepts and practices surrounding measurement uncertainty are important components of physics lab courses. However, there has not been a broadly applicable, research-based assessment tool that allows physics instructors to easily measure students’ knowledge of measurement uncertainty concepts and practices. To address this need, we employed Evidence-Centered Design to create the Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE). SPRUCE is a pre-post assessment instrument intended for use in introductory (first- and second-year) physics lab courses to help instructors and researchers identify student strengths and challenges with measurement uncertainty. In this paper, we discuss the development of SPRUCE’s assessment items guided by Evidence-Centered Design, focusing on how instructors’ and researchers’ assessment priorities were incorporated into the assessment items and how students’ reasoning from pilot testing informed decisions around item answer options. We also present an example of some of the feedback an instructor would receive after implementing SPRUCE in a pre-post fashion, along with a brief discussion of how that feedback could be interpreted and acted upon. © 2023, CC BY.

关键词： Uncertainty analysis

Shape correspondence using anisotropic Chebyshev spectral CNNs

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Shape correspondence using anisotropic Chebyshev spectral CN...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Qinsong Li Shengjun Liu Ling Hu Xinru Liu Institute of Engineering Modeling and Scientific Computing Central South University State Key Laboratory of High Performance Manufacturing Complex Central South University School of Mathematics and Computational Science Hunan First Normal University

ISBN: (数字)9781728171685

ISBN: (纸本)9781728171692

Establishing correspondence between shapes is a very important and active research topic in many domains. Due to the powerful ability of deep learning on geometric data, lots of attractive results have been achieved by convolutional neural networks (CNNs). In this paper, we propose a novel architecture for shape correspondence, termed Anisotropic Chebyshev spectral CNNs (ACSCNNs), based on a new extension of the manifold convolution operator. The extended convolution operators aggregate the local features of signals by a set of oriented kernels around each point, which allows to much more comprehensively capture the intrinsic signal information. Rather than using fixed oriented kernels in the spatial domain in previous CNNs, in our framework, the kernels are learned by spectral filtering, based on the eigen-decompositions of multiple Anisotropic Laplace-Beltrami Operators. To reduce the computational complexity, we employ an explicit expansion of the Chebyshev polynomial basis to represent the spectral filters whose expansion coefficients are trainable. Through the benchmark experiments of shape correspondence, our architecture is demonstrated to be efficient and be able to provide better than the state-of-the-art results in several datasets even if using constant functions as inputs.

关键词： Shape Manifolds Convolution Kernel Machine learning Eigenvalues and eigenfunctions Chebyshev approximation

Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

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arXiv 2022年

作者： Sánchez, Hugo A. Castillo Jovanović, Mihailo R. Kumar, Satish Morozov, Alexander Shankar, V. Subramanian, Ganesh Wilson, Helen J. Department Of Applied Mathematics And Statistics Institute Of Mathematics And Computational Sciences University Of Sao Paulo Brazil Ming Hsieh Department Of Electrical And Computer Engineering University Of Southern California Los AngelesCA90089 United States Department Of Chemical Engineering And Materials Science University Of Minnesota MinneapolisMN55455 United States SUPA School Of Physics And Astronomy The University Of Edinburgh EdinburghEH9 3FD United Kingdom Department Of Chemical Engineering Indian Institute Of Technology Kanpur208016 India Engineering Mechanics Unit Jawaharlal Nehru Center For Advanced Scientific Research Bangalore560064 India Mathematics Department University College London Gower Street LondonWC1E 6BT United Kingdom

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows;(ii) viscometric shearing flows with curved streamlines such as those in the TaylorCouette, cone-and-plate and parallel-plate geometries;(iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device;and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability. © 2022, CC BY.

关键词： Stability

OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

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arXiv 2020年

作者： Yu, Haijun Tian, Xinyuan Weinan, E. Li, Qianxiao NCMIS 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 Department of Mathematics The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics National University of Singapore Singapore119077 Singapore Institute of High Performance Computing A*STAR Singapore138632 Singapore

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative *** Codes 76E30, 34D20, 68T05/07, 82C35 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

Ab initio calculated dynamic structure factors and optical properties of beryllium along the Hugoniot

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arXiv 2023年

作者： Li, Wei-Jie Zhou, Jie Li, Zi Zhu, Yunliang Hu, Han-Dong Ma, Hao Ma, Zhe Wang, Cong Zhang, Ping Intelligent Science & Technology Academy Limited of CASIC Beijing100141 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Scientific Research Key Laboratory of Aerospace Defence Intelligent Systems and Technology Beijing100141 China School of Mechanical and Electric Engineering Sanming University Fujian Province Sanming365004 China Tianfu Innovation Energy Establishment Chengdu610213 China Center for Applied Physics and Technology Peking University Beijing100871 China Shanghai Jiao Tong University 200240 China

Beryllium is an ablator material in the inertial-confinement fusion and hypervelocity impact studies. The thermoelastic properties, structure factors, and optical properties of beryllium are important in these studies. In this paper, the static structure factors, ion-ion dynamic structure factors, adiabatic velocity, and optical properties of beryllium along the Hugoniot were calculated by ab initio simulations. The static structure factors show that beryllium atoms were randomly distributed. The dynamic structure factors via the scattering function have extracted the dispersion relation for the collective excitations. By collecting the peak position of dynamic structure factors, the dispersion relation and adiabatic sound velocity were derived by definitions. By the calculated equation of state, the thermoelastic properties and adiabatic sound velocity have been derived. The two calculated methods about adiabatic sound velocity were verified to be equivalent. © 2023, CC BY.

关键词： Optical properties

Optimal network slicing for service-oriented networks with flexible routing and guaranteed E2E latency

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arXiv 2020年

作者： Chen, Wei-Kun Liu, Ya-Feng de Domenico, Antonio Luo, Zhi-Quan Dai, Yu-Hong The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Huawei Technologies Co. Ltd France Research Center Boulogne-Billancourt92100 France The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

Network function virtualization is a promising technology to simultaneously support multiple services with diverse characteristics and requirements in the 5G and beyond networks. In particular, each service consists of a predetermined sequence of functions, called service function chain (SFC), running on a cloud environment. To make different service slices work properly in harmony, it is crucial to appropriately select the cloud nodes to deploy the functions in the SFC and flexibly route the flow of the services such that these functions are processed in the order defined in the corresponding SFC, the end-to-end (E2E) latency constraints of all services are guaranteed, and all cloud and communication resource budget constraints are respected. In this paper, we first propose a new mixed binary linear program (MBLP) formulation of the above network slicing problem that optimizes the system energy efficiency while jointly considers the E2E latency requirement, resource budget, flow routing, and functional instantiation. Then, we develop another MBLP formulation and show that the two formulations are equivalent in the sense that they share the same optimal solution. However, since the numbers of variables and constraints in the second problem formulation are significantly smaller than those in the first one, solving the second problem formulation is more computationally efficient especially when the dimension of the corresponding network is large. Numerical results demonstrate the advantage of the proposed formulations compared with the existing ones. Copyright © 2020, The Authors. All rights reserved.

关键词： Network function virtualization