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arXiv 2024年

作者： Manna, Satyaki Chaturvedi, Anubhav Saha, Debashis School of Physics Indian Institute of Science Education and Research Kerala Thiruvananthapuram695551 India Faculty of Applied Physics and Mathematics Gdańsk University of Technology Gabriela Narutowicza 11/12 Gdańsk80-233 Poland University of Gdańsk Gdańsk80-308 Poland

Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication complexity relies on the minimal dimension of the communicated systems. In this paper, we measure the communication complexity of a task by the minimal distinguishability required to accomplish it, while leaving the dimension of the communicated systems unconstrained. Distinguishability is defined as the maximum probability of correctly guessing the sender’s input from the message, quantifying the message’s distinctiveness relative to the sender’s input. This measure becomes especially relevant when maintaining the confidentiality of the sender’s input is essential. After establishing the generic framework, we focus on three relevant families of communication complexity tasks—the random access codes, equality problems defined by graphs and the pair-distinguishability tasks. We derive general lower bounds on the minimal classical distinguishability as a function of the success metric of these tasks. We demonstrate that quantum communication outperforms classical communication presenting explicit protocols and utilizing semi-definite programming methods. In particular, we demonstrate unbounded quantum advantage for random access codes and Hadamard graph-based equality problems. Specifically, we show that the classical-to-quantum ratio of minimal distinguishability required to achieve the same success metric escalates polynomially and exponentially with the complexity of these tasks, reaching arbitrarily large values. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum communication

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Unbounded quantum advantage in communication complexity measured by distinguishability

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Physical Review Research 2024年第4期6卷 043269-043269页

作者： Satyaki Manna Anubhav Chaturvedi Debashis Saha School of Physics Indian Institute of Science Education and Research Thiruvananthapuram Kerala 695551 India Faculty of Applied Physics and Mathematics Gdańsk University of Technology Gabriela Narutowicza 11/12 80-233 Gdańsk Poland International Centre for Theory of Quantum Technologies (ICTQT) University of Gdańsk 80-308 Gdańsk Poland

Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication complexity relies on the minimal dimension of the communicated systems. In this paper, we measure the communication complexity of a task by the minimal distinguishability required to accomplish it, while leaving the dimension of the communicated systems unconstrained. Distinguishability is defined as the maximum probability of correctly guessing the sender's input from the message, quantifying the message's distinctiveness relative to the sender's input. This measure becomes especially relevant when maintaining the confidentiality of the sender's input is essential. After establishing the generic framework, we focus on three relevant families of communication complexity tasks—the random access codes, equality problems defined by graphs, and the pair-distinguishability tasks. We derive general lower bounds on the minimal classical distinguishability as a function of the success metric of these tasks. We demonstrate that quantum communication outperforms classical communication presenting explicit protocols and utilizing semidefinite programming methods. In particular, we demonstrate unbounded quantum advantage for random access codes and Hadamard graph-based equality problems. Specifically, we show that the classical-to-quantum ratio of minimal distinguishability required to achieve the same success metric escalates polynomially and exponentially with the complexity of these tasks, reaching arbitrarily large values.

关键词： Quantum communication

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A MgNO Method for Multiphase Flow in Porous Media

arXiv

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arXiv 2024年

作者： Liu, Xinliang Yang, Xia Zhang, Chen-Song Zhang, Lian Zhao, Li Computer Electrical and Mathematical Science and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia Xiangtan University Hunan China LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences University of Chinese Academy of Sciences China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage a variety of crucial factors, such as permeability and porosity heterogeneity. The study extendes MgNO to time-dependent porous media flow problems and validate its accuracy in predicting essential aspects of multiphase flows. Furthermore, the research provides a detailed comparison between MgNO and Fourier Neural Opeartor (FNO), which is one of the most popular neural operator methods, on their performance regarding prediction error accumulation over time. This aspect provides valuable insights into the models' long-term predictive stability and reliability. The study demonstrates MgNO's capability to effectively simulate multiphase flow problems, offering considerable time savings compared to traditional simulation methods, marking an advancement in integrating data-driven methodologies in geoscience applications. © 2024, CC BY.

关键词： Porous materials

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Detecting the Most Probable High Dimensional Transition Pathway Based on Optimal Control Theory

arXiv

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arXiv 2023年

作者： Chen, Jianyu Gao, Ting Li, Yang Duan, Jinqiao Center for Mathematical Sciences Huazhong University of Science and Technology China School of Automation Nanjing University of Science and Technology Nanjing210094 China Departments of Applied Mathematics & Physics Illinois Institute of Technology ChicagoIL60616 United States

Many natural systems exhibit phase transition where external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the behavior of a stochastic dynamic system such as the most probable transition pathway, has made sense. We consider stochastic dynamic systems driven by Brownian motion. Based on variational principle and Onsager-Machlup action functional theory, the variational problem is transformed into deterministic optimal control problem. Different from traditional variational method, optimal control theory can handle high dimensional problems well. This paper describes the following three systems, double well system driven by additive noise, Maire-Stein system driven by multiplicative noise, and Nutrient–Phytoplankton–Nooplanktonr system. For numerical computation, based on Pontryagin’s Maximum Principle, we adopt method of successive approximations to compute the optimal solution pathway, which is the most probable transition pathway in the sense of Onsager-Machlup. Copyright © 2023, The Authors. All rights reserved.

关键词： Maximum principle

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Ferromagnetic impurity induced Majorana zero mode in iron-based superconductors

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Physical Review B 2022年第18期106卷 L180504-L180504页

作者： Rui Song Ping Zhang Xian-Tu He Ning Hao HEDPS Center for Applied Physics and Technology and School of Physics Peking University Beijing 100871 China HEDPS Center for Applied Physics and Technology and School of Engineering Peking University Beijing 100871 China Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions High Magnetic Field Laboratory HFIPS Anhui Chinese Academy of Sciences and University of Science and Technology of China Hefei 230031 China School of Physics and Physical Engineering Qufu Normal University Qufu 273165 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Recent experiments reported the puzzling zero-energy modes associated with ferromagnetic impurities in some iron-based superconductors with topological band structures. Here, we show that a sufficiently strong exchange coupling between a ferromagnetic impurity and a substrate can trigger a quantum phase transition, beyond which the phase of the topological surface superconducting order parameter around the impurity acquires a sign change. In such a case, we prove that besides a pair of impurity induced trivial Yu-Shiba-Rusinov states, a degenerate pair of Majorana modes can be induced at the boundary separating the two sign-change regimes and trapped around the impurity in the topological surface superconducting state. Furthermore, we show that our theory can explain the controversial observations and confusing features of the zero-energy modes from recent experiments in some iron-based superconductors.

关键词： First-principles calculations Superconductivity Topological superconductors Iron-based superconductors

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Kagome Lattice Promotes Chiral Spin Fluctuations

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Physical Review Letters 2023年第13期130卷 136701-136701页

作者： Kamil K. Kolincio Max Hirschberger Jan Masell Taka-hisa Arima Naoto Nagaosa Yoshinori Tokura RIKEN Center for Emergent Matter Science (CEMS) Wako Saitama 351-0198 Japan Faculty of Applied Physics and Mathematics Gdańsk University of Technology Narutowicza 11/12 80-233 Gdańsk Poland Department of Applied Physics and Quantum-Phase Electronics Center (QPEC) The University of Tokyo Bunkyo-ku Tokyo 113-8656 Japan Institute of Theoretical Solid State Physics Karlsruhe Institute of Technology (KIT) 76049 Karlsruhe Germany Department of Advanced Materials Science The University of Tokyo Kashiwa 277-8561 Japan Tokyo College The University of Tokyo Bunkyo-ku Tokyo 113-8656 Japan

Dynamical spin fluctuations in magnets can be endowed with a slight bent toward left- or right-handed chirality by Dzyaloshinskii-Moriya interactions. However, little is known about the crucial role of lattice geometry on these chiral spin fluctuations and on fluctuation-related transport anomalies driven by the quantum-mechanical (Berry) phase of conduction electrons. Via thermoelectric Nernst effect and electric Hall effect experiments, we detect chiral spin fluctuations in the paramagnetic regime of a kagome lattice magnet; these signals are largely absent in a comparable triangular lattice magnet. Supported by Monte Carlo calculations, we identify lattices with at least two dissimilar plaquettes as most promising for Berry phase phenomena driven by thermal fluctuations in paramagnets.

关键词： Anomalous Hall effect Magnetic order Magnetic phase transitions Magnetotransport Nernst effect Phase diagrams Spin dynamics Topological Hall effect Topological phases of matter Chiral magnets Kagome lattice Metals Rare-earth magnetic materials Strongly correlated systems Triangular lattice Crystal growth Hall bar Monte Carlo methods Resistivity measurements Transport techniques

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Automated stopping criterion for spectral measurements with active learning

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npj Computational Materials 2021年第1期7卷 1252-1260页

作者： Tetsuro Ueno Hideaki Ishibashi Hideitsu Hino Kanta Ono Synchrotron Radiation Research Center Kansai Photon Science InstituteQuantum Beam Science Research DirectorateNational Institutes for Quantum and Radiological Science and TechnologySayoHyogoJapan Department of Human Intelligence Systems Graduate School of Life Science and Systems EngineeringKyushu Institute of TechnologyKitakyushuFukuokaJapan The Institute of Statistical Mathematics Research Organization of Information and SystemsTachikawaTokyoJapan Department of Applied Physics Graduate School of EngineeringOsaka UniversitySuitaOsakaJapan Center for Integrative Quantum Beam Science Institute of Materials Structure ScienceHigh Energy Accelerator Research OrganizationTsukubaIbarakiJapan

The automated stopping of a spectral measurement with active learning is *** optimal stopping of the measurement is realised with a stopping criterion based on the upper bound of the posterior average of the generalisation error of the Gaussian process *** is revealed that the automated stopping criterion of the spectral measurement gives an approximated X-ray absorption spectrum with sufficient accuracy and reduced data *** proposed method is not only a proof-of-concept of the optimal stopping problem in active learning but also the key to enhancing the efficiency of spectral measurements for highthroughput experiments in the era of materials informatics.

关键词： criterion spectral optimal

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(f,Γ)-Divergences: Interpolating between f-Divergences and Integral Probability Metrics

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Journal of Machine Learning Research 2022年 23卷

作者： Birrell, Jeremiah Dupuis, Paul Katsoulakis, Markos A. Pantazis, Yannis Rey-Bellet, Luc TRIPODS Institute for Theoretical Foundations of Data Science University of Massachusetts Amherst AmherstMA01003 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Mathematics and Statistics University of Massachusetts Amherst AmherstMA01003 United States Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas HeraklionGR-70013 Greece

We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both f-divergences and integral probability metrics (IPMs), such as the 1-Wasserstein distance. We prove under which assumptions these divergences, hereafter referred to as (f, Γ)-divergences, provide a notion of 'distance' between probability measures and show that they can be expressed as a two-stage mass-redistribution/mass-transport process. The (f, Γ)-divergences inherit features from IPMs, such as the ability to compare distributions which are not absolutely continuous, as well as from f-divergences, namely the strict concavity of their variational representations and the ability to control heavy-tailed distributions for particular choices of f. When combined, these features establish a divergence with improved properties for estimation, statistical learning, and uncertainty quantification applications. Using statistical learning as an example, we demonstrate their advantage in training generative adversarial networks (GANs) for heavy-tailed, not-absolutely continuous sample distributions. We also show improved performance and stability over gradient-penalized Wasserstein GAN in image generation. © 2022 Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Yannis Pantazis, and Luc Rey-Bellet.

关键词： Generative adversarial networks

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Stretched Non-negative Matrix Factorization

arXiv

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arXiv 2023年

作者： Gu, Ran Rakita, Yevgeny Lan, Ling Thatcher, Zach Kamm, Gabrielle E. O’Nolan, Daniel McBride, Brennan Wustrow, Allison Neilson, James R. Chapman, Karena W. Du, Qiang Billinge, Simon J.L. School of Statistics and Data Science Nankai University Tianjin300071 China Department of Applied Physics and Applied Mathematics Fu Foundation School of Engineering & Applied Sciences Columbia University New YorkNY10025 United States Department of Chemistry Stony Brook University Stony BrookNY11794 United States Department of Chemistry Colorado State University Fort CollinsCO80523 United States

An algorithm is described and tested that carries out a non negative matrix factorization (NMF) ignoring any stretching of the signal along the axis of the independent variable. This extended NMF model is called stretchedNMF. Variability in a set of signals due to this stretching is then ignored in the decomposition. This can be used, for example, to study sets of powder diffraction data collected at different temperatures where the materials are undergoing thermal expansion. It gives a more meaningful decomposition in this case where the component signals resemble signals from chemical components in the sample. The stretchedNMF model introduces a new variable, the stretching factor, to describe any expansion of the signal. To solve stretchedNMF, we discretize it and employ Block Coordinate Descent framework algorithms. The initial experimental results indicate that stretchedNMF model outperforms the conventional NMF for sets of data with such an expansion. A further enhancement to stretchedNMF for the case of powder diffraction data from crystalline materials called sparse-stretchedNMF, which makes use of the sparsity of the powder diffraction signals, allows correct extractions even for very small stretches where stretchedNMF struggles. As well as demonstrating the model performance on simulated PXRD patterns and atomic pair distribution functions (PDFs), it also proved successful when applied to real data taken from an in situ chemical reaction experiment. Copyright © 2023, The Authors. All rights reserved.

关键词： Non-negative matrix factorization

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Bias Tunable and High Temperature Characteristics in Ratchet Detector

Bias Tunable and High Temperature Characteristics in Ratchet...

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Cross Strait Quad-Regional Radio science and Wireless Technology Conference (CSRWTC)

作者： Yi Wang Shangjie Han Jiaxuan Cai Peng Bai Ning Yang Weidong Chu Xiaohong Li Yueheng Zhang Yan Xie Meng Chen Yingxin Wang Ziran Zhao School of Information Science and Technology North China University of Technology Beijing China Institute of Applied Physics and Computational Mathematics Beijing China School of Physics and Astronomy Shanghai Jiao Tong University Shanghai China Department of Engineering Physics Tsinghua University Beijing China

The ratchet effect has promising applications in radiation detection. We propose a ratchet structure that can achieve broadband terahertz (THz) detection. In this paper, we focus on the bias-tunable characteristics of the ratchet structure and its high-temperature operating characteristics. We give the photocurrent spectrum response characteristics of the device under different bias voltages and analyze the reasons for the bias-dependent characteristics. The response photocurrent results of the device to the blackbody under different bias voltages are also analyzed. The high operating temperature characteristics of the device under zero bias are also given.

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