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Quantum noise protects quantum classifiers against adversaries

Physical Review Research 2021年第2期3卷 023153-023153页

作者： Yuxuan Du Min-Hsiu Hsieh Tongliang Liu Dacheng Tao Nana Liu UBTECH Sydney AI Centre School of Computer Science Faculty of Engineering University of Sydney Australia Hon Hai Quantum Computing Research Center No. 32 Jihu Road Neihu District Taipei 114 Taiwan Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai 200240 China

Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing? An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as worst-case perturbations by unknown noise sources. We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy. For the protection of quantum data, this quantum protocol can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data. This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.

关键词： Machine learning Quantum algorithms Quantum information processing Quantum protocols

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Capacity optimality of AMP in coded systems

arXiv

引用

arXiv 2021年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Department of Electronic Engineering City University of Hong Kong Hong Kong School of Information Science Japan Institute of Science and Technology Nomi923-1292 Japan State Key Laboratory of Mobile Network and Mobile Multimedia Technology ZTE Corporation Shenzhen518057 China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences 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. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over unmatched 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. © 2021, CC BY-NC-SA.

关键词： Message passing

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MAP-based Problem-Agnostic Diffusion Model for Inverse Problems

arXiv

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arXiv 2025年

作者： Tao, Pingping Liu, Haixia Su, Jing Yang, Xiaochen Tan, Hongchen Shandong University Library No. 180 West Culture Road Shandong Weihai264209 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology No. 1037 Luoyu road Hubei Wuhan430074 China Dapartment of Basic Sciences Dalian University of Science and Technology No. 999-26 Harbor Road Liaoning Dalian116052 China School of Computer Science and Technology Harbin Institute of Technology No. 2 West Culture Road Shandong Weihai264209 China Institute of Future Technology Dalian University of Technology No. 2 Lingong Road Liaoning Dalian116081 China

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes’ rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods—for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting. Our numerical implementation is available at https://***/liuhaixias1/ MAP-DIFFUSION-IP. Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

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RIGIDITY OF STEADY SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN HIGH DIMENSIONS AND ITS APPLICATIONS

arXiv

引用

arXiv 2023年

作者： Bang, Jeaheang Gui, Changfeng Liu, Hao Wang, Yun Xie, Chunjing Department of Mathematics The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Department of Mathematics Faculty of Science and Technology University of Macau Taipa China School of Mathematical Sciences Institute of Natural Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

Solutions with scaling-invariant bounds such as self-similar solutions, play an important role in the understanding of the regularity and asymptotic structures of solutions to the Navier-Stokes equations. In this paper, we prove that any steady solution satisfying |u(x)| ≤ C/|x| for any constant C in n \ {0} with n ≥ 4, must be zero. Our main idea is to analyze the velocity field and the total head pressure via weighted energy estimates with suitable multipliers so that the proof is pretty elementary and short. These results not only give the Liouville-type theorem for steady solutions in higher dimensions with neither smallness nor self-similarity type assumptions, but also help to remove a class of singularities of solutions and give the optimal asymptotic behaviors of solutions at infinity in the exterior domains. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Combined influences of Soret effect and horizontal magnetic field on dynamics of vertical convection in binary fluids

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Physical Review Fluids 2025年第5期10卷 053503-053503页

作者： Chao-Nan Zhang Lai-yun Zheng Xu-Long Li Juan-Juan Qin Bing-Xin Zhao Don Liu School of Mathematics and Statistics Ningxia University Yinchuan 750021 China School of Mechanical Engineering Ningxia University Yinchuan 750021 China Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Yinchuan 750021 China Ningxia Basic Science Research Center of Mathematics Yinchuan 750021 China Department of Mathematics and Mechanical Engineering Louisiana Tech University Ruston Louisiana 71270 USA

The influence of the Soret effect and a uniform magnetic field on the dynamic behavior of vertical convection are investigated using a high-accuracy numerical method. The effects of the Soret number (Sr, which quantifies the direction and magnitude of species migration relative to the temperature gradient; positive Sr denotes migration toward hotter regions, negative toward cooler regions) on flow, heat and mass transfer, and flow transition in the presence of a magnetic field are analyzed. The results reveal that, for a given magnetic field strength, positive and negative Soret effects have significantly different influences on heat and mass transfer as well as on flow structure. For a high Rayleigh number (Ra, vigor of the buoyancy) and a small magnetic field, the heat transfer initially decreases and then increases with increasing Soret number, while the mass transfer consistently decreases. In cases where temperature is dominant, heat transfer for Sr=−1 exceeds that for Sr=0 by 24%, while mass transfer with Sr=−1 exceeds that for Sr=0 by 85%. When concentration is dominant, heat transfer reaches a minimum at Sr=0, whereas mass transfer peaks at Sr=−1, corresponding to an approximate 71% increase over heat transfer at Sr=0, and around a 210% increase in mass transfer. Additionally, the flow exhibits greater complexity when the Soret number is negative than when it is positive. When the magnetic field is weak, the temperature-dominated flow changes from chaotic to periodic with increasing Soret number and eventually returns to a chaotic state. When the magnetic field is strong, the flow transitions from chaotic to periodic and finally to a steady state. The transition route involves two types of periodic flow: a simple periodic flow with an integer multiple of the fundamental frequency, and a complex periodic flow with multiple lower-frequency subharmonic waves. Furthermore, as the strength of the magnetic field increases, the flow in the rectangular enclosure is

关键词： Diffusion in solids

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A structure-preserving numerical scheme for non-isothermal compressible flow in porous media: Energy conservation and entropy stability

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Physics of Fluids 2025年第5期37卷

作者： Kou, Jisheng Chen, Huangxin Sun, Shuyu Wang, Xiuhua School of Civil Engineering Shaoxing University Zhejiang Shaoxing312000 China School of Mathematics and Statistics Hubei Engineering University Hubei Xiaogan432000 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian Xiamen361005 China School of Mathematical Sciences Tongji University Shanghai200092 China

Numerical simulation of non-isothermal flow in porous media has great applications in unconventional gas recovery. Reliable and promising numerical methods should be compatible with the first and second laws of thermodynamics. Toward this goal, by taking molar density and temperature as the primary unknowns, we propose an alternative formulation of the realistic non-isothermal gas flow model, which is proved to obey the first and second laws of thermodynamics. On the basis of this formulation, we propose an energy conservative and entropy stable numerical scheme;that is, the scheme can preserve the first law of thermodynamics (the energy conservation law) as well as the second law of thermodynamics (entropy stability). An important ingredient of the scheme is to derive a new discrete chemical potential utilizing the energy factorization approach, which can preserve the dissipation of original Helmholtz free energy. Some subtle temporal and spatial treatments have also been introduced to deal with the inherent coupling relationships between multiple variables. Using the local analysis method, we prove that the scheme can be compatible with both local and global forms of the first and second laws of thermodynamics. Numerical results validate our theoretical analysis and demonstrate conservative and stable features of the proposed scheme. © 2025 Author(s).

关键词： Entropy

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Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

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Science China(Physics,Mechanics & Astronomy) 2018年第1期61卷 57-67页

作者： XiaoXu Zhong ShiJun Liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration State Key Laboratory of Ocean Engineering Ministry-of-Education Key Laboratory of Scientific and Engineering Computing

Analytic approximations of the Von Karman＇s plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method （HAM）, an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c1 and c2 in the frame of the HAM. Besides, it is found that the HAM- based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c1= -0 and c2 = -1, where 0 denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c1 = -0 and c2= -1. In addition, we prove that the HAM approach for the Von karman＇s plate equations in differential form is just a special case of the HAM for the Von karman＇s plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

关键词： circular plate high nonlinearity homotopy analysis method

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Probabilistic methods for approximate archetypal analysis

arXiv

引用

arXiv 2021年

作者： Han, Ruijian Osting, Braxton Wang, Dong Xu, Yiming Department of Statistics The Chinese University of Hong Kong Hong Kong Department of Mathematics University of Utah Salt Lake City United States School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Guangdong Provincial Key Laboratory of Big Data Computing The Chinese University of Hong Kong Shenzhen China Scientific Computing and Imaging Institute University of Utah Salt Lake City United States

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided the data is approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of archetypal analysis. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of archetypal analysis. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets. Copyright © 2021, The Authors. All rights reserved.

关键词： Large dataset

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Phase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows

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Physical Review E 2020年第6期101卷 063310-063310页

作者： Xiaolei Yuan Hong Liang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China Department of Physics Hangzhou Dianzi University Hangzhou 310018 China

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase flows (N≥2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N−1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N≥2) immiscible incompressible flows.

关键词： Multiphase flows Lattice-Boltzmann methods

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Phase transition analysis for covariance based massive random access with massive MIMO

arXiv

引用

arXiv 2020年

作者： Chen, Zhilin Sohrabi, Foad Liu, Ya-Feng Yu, Wei The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada 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

This paper considers a massive random access problem in which a large number of sporadically active devices wish to communicate with a base station (BS) equipped with massive multiple-input multiple-output (MIMO) antennas. Each device is preassigned a unique signature sequence, and the BS identifies the active devices by detecting which sequences are transmitted. This device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem for which the sample covariance matrix of the received signal is a sufficient statistic. The goal of this paper is to characterize the feasible set of problem parameters under which this covariance based approach is able to successfully recover the device activities in the massive MIMO regime. Through an analysis of the asymptotic behaviors of MLE via its associated Fisher information matrix, this paper derives a necessary and sufficient condition on the Fisher information matrix to ensure a vanishing probability of detection error as the number of antennas goes to infinity, based on which a numerical phase transition analysis is obtained. This condition is also examined from a perspective of covariance matching, which relates the phase transition analysis to a recently derived scaling law. Further, we provide a characterization of the distribution of the estimation error in MLE, based on which the error probabilities in device activity detection can be accurately predicted. Finally, this paper studies a random access scheme with joint device activity and data detection and analyzes its performance in a similar way. Copyright © 2020, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

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