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arXiv 2022年

作者： Lei, Zhu Zhao, Z.H. Li, X.Y. Li, L.X. Xie, Y. Yuan, W.Q. Zhu, B.Q. Zhu, J.Q. Zhu, S.P. He, X.T. Qiao, B. Center for Applied Physics and Technology HEDPS State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University Beijing100871 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Department of Plasma Physics and Fusion Engineering CAS Key Laboratory of Geospace Environment University of Science and Technology of China Anhui Hefei230026 China National Laboratory on High Power Laser and Physics Chinese Academy of Sciences Shanghai201800 China

The interaction between a jet and its surrounding medium plays a crucial role in various astrophysical phenomena, notably in star formation and jet deflection. Despite its significance, the detailed processes and fine shock structures involved in this interaction remain elusive due to limitations in current astronomical facilities, such as the confusing HCO+ emission in the Herbig-Haro (HH) 110/270 system. Here, we investigate the scaled plasma dynamics of this interaction under different collision states using laser-driven experiments. The experimental results demonstrate the importance of collision in jet deflection, revealing a distinctive double-shock structure in collision cases and a double-emission-shell structure in cases of strong collisions. Both cases exhibit a notable deflection of plasma jets by 50◦ as a consequence of interaction with a high-density background. Optical images confirm that the impact point can be pushed into the inside part of the background medium, consistent with previous astrophysical models and simulations. In contrast, collisionless cases exhibit filament structures (the ion skin depth scale), yet there is an absence of discernible deflection in the direction of jet transmission. Furthermore, our findings have implications for understanding the shock structure in the HH 110/270 system. The significant HCO+ emission observed west of HH 110 may be attributed to the impact point being pushed into the inside part of the background. Copyright © 2022, The Authors. All rights reserved.

关键词： Astrophysics

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Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution

arXiv

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arXiv 2023年

作者： Kökcü, Efekan Camps, Daan Oftelie, Lindsay Bassman de Jong, Wibe A. Van Beeumen, Roel Kemper, A.F. Department of Physics North Carolina State University RaleighNC27695 United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions [1, 2]. The compression algorithm yields a circuit which scales linearly in the number of qubits, is fixed depth for for arbitrarily long evolution times and is applicable to time dependent Hamiltonians, although is limited to simple nearest-neighbor spin interactions and fermionic hopping. In this work, we extend the algorithm to compress circuits simulating evolution with long-range spin interactions and fermionic hopping, thereby enabling embedding of arbitrary lattices onto a chain of qubits. Moreover, we show that controlled time evolution, as well as fermion creation and annihilation operators can also be compressed. We demonstrate our results by adiabatically preparing the ground state for a half-filled fermionic chain, and simulating a 4×4 tight binding model on ibmq washington. With these new developments, our results enable the simulation of a wider range of models of interest and the efficient compression of subcircuits. Copyright © 2023, The Authors. All rights reserved.

关键词： Ground state

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KOLMOGOROV WIDTH DECAY AND POOR APPROXIMATORS IN MACHINE LEARNING: SHALLOW NEURAL NETWORKS, RANDOM FEATURE MODELS AND NEURAL TANGENT KERNELS

arXiv

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arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544

We establish a scale separation of Kolmogorov width type between subspaces of a given Banach space under the condition that a sequence of linear maps converges much faster on one of the subspaces. The general technique is then applied to show that reproducing kernel Hilbert spaces are poor L2-approximators for the class of two-layer neural networks in high dimension, and that two-layer networks with small path norm are poor approximators for certain Lipschitz functions, also in the *** Codes 68T07, 41A30, 41A65, 46E15, 46E22 Copyright © 2020, The Authors. All rights reserved.

关键词： Banach spaces

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Coarse-grained spectral projection (CGSP): A deep learning-assisted approach to quantum unitary dynamics

arXiv

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arXiv 2020年

作者： Xie, Pinchen Weinan, E. Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We propose the coarse-grained spectral projection method (CGSP), a deep learning-assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show CGSP can extract spectral components of many-body quantum states systematically with sophisticated neural network quantum ansatz. CGSP exploits fully the linear unitary nature of the quantum dynamics, and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on 1D XXZ models with periodic boundary condition are carried out to demonstrate the practicality of CGSP. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamics

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DeePKS-kit: A package for developing machine learning-based chemically accurate energy and density functional models

arXiv

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arXiv 2020年

作者： Chen, Yixiao Zhang, Linfeng Wang, Han Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ United States

We introduce DeePKS-kit, an open-source software package for developing machine learning based energy and density functional models. DeePKS-kit is interfaced with PyTorch, an open-source machine learning library, and PySCF, an ab initio computational chemistry program that provides simple and customized tools for developing quantum chemistry codes. It supports the DeePHF and DeePKS methods. In addition to explaining the details in the methodology and the software, we also provide an example of developing a chemically accurate model for water clusters. Copyright © 2020, The Authors. All rights reserved.

关键词： Electronic structure

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DeePKS: A comprehensive data-driven approach towards chemically accurate density functional theory

arXiv

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arXiv 2020年

We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training self-consistent models that are capable of taking large datasets from different systems and different kinds of labels. We demonstrate that the functional that results from this training procedure gives chemically accurate predictions on energy, force, dipole, and electron density for a large class of molecules. It can be continuously improved when more and more data are available. Copyright © 2020, The Authors. All rights reserved.

关键词： Large dataset

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Regimes of stratified turbulence at low Prandtl number

arXiv

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arXiv 2023年

作者： Shah, Kasturi Chini, Gregory P. Caulfield, Colm-Cille P. Garaud, Pascale Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Department of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institute for Energy and Environmental Flows University of Cambridge CambridgeCB3 0EZ United Kingdom Department of Applied Mathematics Baskin School of Engineering University of California Santa Cruz Santa CruzCA95064 United States

Quantifying transport by strongly stratified turbulence in low Prandtl number (Pr) fluids is critically important for the development of better models for the structure and evolution of stellar and planetary interiors. Motivated by recent numerical simulations showing strongly anisotropic flows suggestive of scale-separated dynamics, we perform a multiscale asymptotic analysis of the governing equations. We find that, in all cases, the resulting slow-fast systems take a quasilinear form. Our analysis also reveals the existence of several distinct dynamical regimes depending on the emergent buoyancy Reynolds and Péclet numbers, Reb = α2Re and Peb = PrReb, respectively, where α is the aspect ratio of the large-scale turbulent flow structures, and Re is the outer scale Reynolds number. Scaling relationships relating the aspect ratio, the characteristic vertical velocity, and the strength of the stratification (measured by the Froude number Fr) naturally emerge from the analysis. When Peb α, the dynamics at all scales is dominated by buoyancy diffusion, and our results recover the scaling laws empirically obtained from direct numerical simulations by Cope et al. (2020). For Peb ≥ O(1), diffusion is negligible (or at least subdominant) at all scales and our results are consistent with those of Chini et al. (2022) for strongly stratified geophysical turbulence at Pr = O(1). Finally, we have identified a new regime for α Peb 1, in which slow, large scales are diffusive while fast, small scales are not. We conclude by presenting a map of parameter space that clearly indicates the transitions between isotropic turbulence, non-diffusive stratified turbulence, diffusive stratified turbulence and viscously-dominated flows, and by proposing parameterisations of the buoyancy flux, mixing efficiency and turbulent diffusion coefficient for each regime. © 2023, CC BY.

关键词： Buoyancy

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Fast Universal Entangling Gate for Superconducting Quantum Computers

SSRN

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SSRN 2024年

作者： AbuGhanem, Muhammad Homid, Ali H. Obada, A.S.-F. Hendy, Ahmed S. Eleuch, Hichem Faculty of Science Ain Shams University Cairo11566 Egypt Zewail City of Science Technology and Innovation Giza12678 Egypt Mathematics Department Faculty of Science Al-Azhar University Assiut71524 Egypt Mathematics Department Faculty of Science Al-Azher University Nassr City Cairo11884 Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University Yekaterinburg Russia Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Applied Physics and Astronomy University of Sharjah Sharjah27272 United Arab Emirates College of Arts and Sciences Abu Dhabi University Abu Dhabi59911 United Arab Emirates Institute for Quantum Science and Engineering Texas A&M University College StationTX77843 United States

Universal quantum gates are crucial for efficient algorithm execution on quantum computers, offering rapid and fault-tolerant manipulations. This paper presents a theoretical framework for realizing a novel entangling universal quantum gate within the circuit quantum electrodynamics (circuit QED) architecture. Our approach involves positioning two SQUIDs qubits within a resonant single-mode microwave cavity field, enabling the implementation of the SQSCZ gate, a fusion of the square root of SWAP ($\sqrt{SWAP}$) and the square root of controlled-Z ($\sqrt{CZ}$) gates. This gate serves as a fundamental building block for constructing universal quantum gates including the controlled-NOT gates. Moreover, the SQSCZ gate operates unitarily, ensuring logical reversibility, and exhibits an entangling power (EP) of 1.5/9. Quantitative analysis reveals an average gate fidelity of $60\%$. To delve deeper into the gate's performance, we conducted quantum process tomography (QPT) analysis by repeating the quantum experiment 11,000 times for each measurement basis on an IBM Quantum's quantum simulator. This rigorous approach yielded a remarkable process fidelity of $96.065616\%$. These findings offer promising implications for future research and applications. © 2024, The Authors. All rights reserved.

关键词： Qubits

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Ground state energy functional with Hartree-Fock efficiency and chemical accuracy

arXiv

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arXiv 2020年

We introduce the Deep Post–Hartree–Fock (DeePHF) method, a machine learning-based scheme for constructing accurate and transferable models for the ground-state energy of electronic structure problems. DeePHF predicts the energy difference between results of highly accurate models such as the coupled cluster method and low accuracy models such as the the Hartree-Fock (HF) method, using the ground-state electronic orbitals as the input. It preserves all the symmetries of the original high accuracy model. The added computational cost is less than that of the reference HF or DFT and scales linearly with respect to system size. We examine the performance of DeePHF on organic molecular systems using publicly available datasets and obtain the state-of-art performance, particularly on large datasets. Copyright © 2020, The Authors. All rights reserved.

关键词： Molecular physics

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Bayesian calibration of viscous anisotropic hydrodynamic simulations of heavy-ion collisions

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Physical Review C 2023年第5期108卷 054905-054905页

作者： Dananjaya Liyanage Özge Sürer Matthew Plumlee Stefan M. Wild Ulrich Heinz Department of Physics The Ohio State University Columbus Ohio 43210 USA Department of Information Systems and Analytics Miami University Oxford Ohio 45056 USA Northwestern-Argonne Institute of Science and Engineering (NAISE) Northwestern University Evanston Illinois 60208 USA Industrial Engineering and Management Sciences Department Northwestern University Evanston Illinois 60208 USA Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

Owing to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until O(1) fm/c after the collision. To address this one often introduces a prehydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the prehydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopically using the recently developed viscous anisotropic hydrodynamics (VAH). In high-energy heavy-ion collisions VAH is applicable already at very early times, and at later times transitions smoothly into conventional second-order viscous hydrodynamics. We present a Bayesian calibration of the VAH model with experimental data for Pb-Pb collisions at the LHC at sNN=2.76 TeV. We find that the VAH model has the unique capability of constraining the specific viscosities of the quark-gluon plasma at higher temperatures than other previously used models.

关键词： Charged-particle multiplicity Collective flow Quark-gluon plasma Relativistic heavy-ion collisions Transport in heavy-ion collisions

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