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Efficient explicit gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations

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arXiv 2024年

作者： Guseynov, Nikita Huang, Xiajie Liu, Nana University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China Institute of Natural Sciences School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

One of the most promising applications of quantum computers is solving partial differential equations (PDEs). By using the Schrödingerisation technique — which converts non-conservative PDEs into Schrödinger equations – the problem can be reduced to Hamiltonian simulations. The particular class of Hamiltonians we consider is shown to be sufficient for simulating almost any linear PDE. In particular, these Hamiltonians consist of discretizations of polynomial products and sums of position and momentum operators. This paper addresses an important gap by efficiently loading these Hamiltonians into the quantum computer through block-encoding. The construction is explicit and efficient in terms of one- and two-qubit operations, forming a fundamental building block for constructing the unitary evolution operator for that class of Hamiltonians. The proposed algorithm demonstrates a squared logarithmic scaling with respect to the spatial partitioning size, offering a polynomial speedup over classical finite-difference methods in the context of spatial partitioning for PDE solving. Furthermore, the algorithm is extended to the multi-dimensional case, achieving an exponential acceleration with respect to the number of dimensions, alleviating the curse of dimensionality problem. This work provides an essential foundation for developing explicit and efficient quantum circuits for PDEs, Hamiltonian simulations, and ground state and thermal state *** Codes 68Q12 © 2024, CC BY.

关键词： Hamiltonians

Transductive Matrix Completion with Calibration for Multi-Task Learning

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arXiv 2023年

作者： Wang, Hengfang Zhang, Yasi Mao, Xiaojun Wang, Zhonglei School of Mathematics and Statistics Fujian Normal University China Department of Statistics University of California Los Angeles United States School of Mathematical Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University China Wang Yanan Institute for Studies in Economics School of Economics Xiamen University China

Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. Moreover, transduction with matrix completion is a useful method in multi-label learning. In this paper, we propose a transductive matrix completion algorithm that incorporates a calibration constraint for the features under the multi-task learning framework. The proposed algorithm recovers the incomplete feature matrix and target matrix simultaneously. Fortunately, the calibration information improves the completion results. In particular, we provide a statistical guarantee for the proposed algorithm, and the theoretical improvement induced by calibration information is also studied. Moreover, the proposed algorithm enjoys a sub-linear convergence rate. Several synthetic data experiments are conducted, which show the proposed algorithm out-performs other existing methods, especially when the target matrix is associated with the feature matrix in a nonlinear way. Copyright © 2023, The Authors. All rights reserved.

关键词： Calibration

THERMODYNAMIC FORMALISM FOR CORRESPONDENCES

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arXiv 2023年

作者： Li, Xiaoran Li, Zhiqiang Zhang, Yiwei School of Mathematical Sciences Peking University Beijing100871 China School of Mathematical Sciences Beijing International Center for Mathematical Research Peking University Beijing100871 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this work, we investigate the Variational Principle and develop a thermodynamic formalism for correspondences. We define the measure-theoretic entropy for transition probability kernels and topological pressure for correspondences. Based on these two notions, we establish the following results: The Variational Principle holds and equilibrium states exist for continuous potential functions, provided that the correspondence satisfies some expansion property called forward expansiveness. If, in addition, the correspondence satisfies the specification property and the potential function is Bowen summable, then the equilibrium state is unique. On the other hand, for a distance-expanding, open, strongly transitive correspondence and a Hölder continuous potential function, there exists a unique equilibrium state, and the backward orbits are equidistributed. Furthermore, we investigate the Variational Principle for general correspondences. In conformal dynamics, we establish the Variational Principle for the Lee-Lyubich-Markorov-Mazor-Mukherjee anti-holomorphic correspondences, which are matings of some anti-holomorphic rational maps with anti-Hecke groups and not forward expansive. We also show a Ruelle-Perron-Frobenius Theorem for a family of hyperbolic holomorphic correspondences of the form fc(z) = zq/p + *** Codes Primary: 37F05, Secondary: 54C60, 37D35, 37C30, 37D20 Copyright © 2023, The Authors. All rights reserved.

关键词： Thermodynamics

Sampling-Based Methods for Multi-Block Optimization Problems over Transport Polytopes

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arXiv 2023年

作者： Hu, Yukuan Li, Mengyu Liu, Xin Meng, Cheng State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China Institute of Statistics and Big Data Renmin University of China Beijing China Center for Applied Statistics Institute of Statistics and Big Data Renmin University of China Beijing China

This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for the general multi-block problems store and operate on the matrix variables directly, resulting in formidable expenditure for large-scale settings. On the other hand, optimal transport problems, as a special case, have attracted extensive attention and numerical techniques that waive the use of the full matrices have recently emerged. However, it remains nontrivial to apply these techniques to the multi-block, possibly nonconvex problems with theoretical guarantees. In this work, we leverage the benefits of both sides and develop novel sampling-based block coordinate descent-type methods, which are equipped with either entropy regularization or Kullback-Leibler divergence. Each iteration of these methods solves subproblems restricted on the sampled degrees of freedom. Consequently, they involve only sparse matrices, which amounts to considerable complexity reductions. We explicitly characterize the sampling-induced errors and establish convergence and asymptotic properties for the methods equipped with the entropy regularization. Numerical experiments on typical strongly correlated electron systems corroborate their superior scalability over the methods utilizing full matrices. The advantage also enables the first visualization of approximate optimal transport maps between electron positions in three-dimensional *** Codes 52-08, 65C05, 65F50, 81V05, 90C30 © 2023, CC BY.

关键词： Entropy

Non-Hermitian lattice fermions in the 2D Gross-Neveu-Yukawa model

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Physical Review D 2024年第3期110卷 034502-034502页

作者： Xingyu Guo Chen-Te Ma Hui Zhang Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE) Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter Institute of Quantum Matter South China Normal University Department of Physics and Astronomy Iowa State University Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum Matter South China Normal University Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing Center South China Normal University Asia Pacific Center for Theoretical Physics Pohang University of Science and Technology School of Physics and Telecommunication Engineering South China Normal University The Laboratory for Quantum Gravity and Strings Department of Mathematics and Applied Mathematics University of Cape Town Physics Department Center for Exploration of Energy and Matter Indiana University

We work the lattice fermions and non-Hermitian formulation in the 2D Gross-Neveu-Yukawa (GNY) model and demonstrate the numerical implementation for two flavors by the hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the nonsymmetrized finite-difference operator. We restore the hypercubic symmetry by averaging over all possible orientations with the proper continuum limit. Our study is the first simulation for the interacting fermion formulated in a non-Hermitian way. We compare the numerical solution with the one-loop resummation. The resummation results matches with the numerical solution in ⟨ϕ⟩, ⟨ϕ2⟩, ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)/2⟩, and ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)ϕ/2⟩. We also used the one-loop resummation to provide the renormalization group flow and asymptotic safety in the 2D GNY model.

关键词： Nonperturbative effects in field theory Perturbation theory Chiral symmetry Hybrid Monte Carlo algorithm Lattice field theory

AppealNet: An Efficient and Highly-Accurate Edge/Cloud Collaborative Architecture for DNN Inference 21

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AppealNet: An Efficient and Highly-Accurate Edge/Cloud Colla...

Proceedings of the 58th Annual ACM/IEEE Design Automation Conference

作者： Min Li Yu Li Ye Tian Li Jiang Qiang Xu CUhk REliable Computing Laboratory (CURE). Department of Computer Science and Engineering The Chinese University of Hong Kong Shatin Hong Kong S.A.R. Department of Computer Science and Engineering MoE Key Lab of Artificial Intelligence AI Institute Shanghai Jiao Tong University Shanghai China

ISBN: (纸本)9781665432740

This paper presents AppealNet, a novel edge/cloud collaborative architecture that runs deep learning (DL) tasks more efficiently than state-of-the-art solutions. For a given input, AppealNet accurately predicts on-the-fly whether it can be successfully processed by the DL model deployed on the resource-constrained edge device, and if not, appeals to the more powerful DL model deployed at the cloud. This is achieved by employing a two-head neural network architecture that explicitly takes inference difficulty into consideration and optimizes the tradeoff between accuracy and computation/communication cost of the edge/cloud collaborative architecture. Experimental results on several image classification datasets show up to more than 40% energy savings compared to existing techniques without sacrificing accuracy.

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Quality Metric Guided Portrait Line Drawing Generation from Unpaired Training Data

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arXiv 2022年

作者： Yi, Ran Liu, Yong-Jin Lai, Yu-Kun Rosin, Paul L. BNRist MOE-Key Laboratory of Pervasive Computing The Department of Computer Science and Technology Tsinghua University Beijing China Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai China School of Computer Science and Informatics Cardiff University United Kingdom

Face portrait line drawing is a unique style of art which is highly abstract and expressive. However, due to its high semantic constraints, many existing methods learn to generate portrait drawings using paired training data, which is costly and time-consuming to obtain. In this paper, we propose a novel method to automatically transform face photos to portrait drawings using unpaired training data with two new features;i.e., our method can (1) learn to generate high quality portrait drawings in multiple styles using a single network and (2) generate portrait drawings in a "new style" unseen in the training data. To achieve these benefits, we (1) propose a novel quality metric for portrait drawings which is learned from human perception, and (2) introduce a quality loss to guide the network toward generating better looking portrait drawings. We observe that existing unpaired translation methods such as CycleGAN tend to embed invisible reconstruction information indiscriminately in the whole drawings due to significant information imbalance between the photo and portrait drawing domains, which leads to important facial features missing. To address this problem, we propose a novel asymmetric cycle mapping that enforces the reconstruction information to be visible and only embedded in the selected facial regions. Along with localized discriminators for important facial regions, our method well preserves all important facial features in the generated drawings. Generator dissection further explains that our model learns to incorporate face semantic information during drawing generation. Extensive experiments including a user study show that our model outperforms state-of-the-art methods. Copyright © 2022, The Authors. All rights reserved.

关键词： Generative adversarial networks

MSTC^∗:Multi-robot Coverage Path Planning under Physical Constrain

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MSTC<sup>∗</sup>:Multi-robot Coverage Path Planning under P...

IEEE International Conference on Robotics and Automation (ICRA)

作者： Jingtao Tang Chun Sun Xinyu Zhang Shanghai Key Laboratory of Trustworthy Computing Engineering Research Center of Software/Hardware Co-Design Technology and Application (MoE) and School of Software Engineering East China Normal University Shanghai

For large-scale tasks, coverage path planning (CPP) can benefit greatly from multiple robots. In this paper, we present an efficient algorithm MSTC∗ for multi-robot coverage path planning (mCPP) based on spiral spanni... 详细信息

For large-scale tasks, coverage path planning (CPP) can benefit greatly from multiple robots. In this paper, we present an efficient algorithm MSTC^∗ for multi-robot coverage path planning (mCPP) based on spiral spanning tree coverage (Spiral-STC). Our algorithm incorporates strict physical constraints like terrain traversability and material load capacity. We compare our algorithm against the state-of-the-art in mCPP for regular grid maps and real field terrains in simulation environments. The experimental results show that our method significantly outperforms existing spiral-STC based mCPP methods. Our algorithm can find a set of well-balanced workload distributions for all robots and therefore, achieve the overall minimum time to complete the coverage.

关键词： Spirals Automation Conferences Path planning Task analysis Robots Load modeling

Unveiling the corrosion evolution and pitting mechanism of X70 pipeline steel in typical near-neutral/bentonite soil environment

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Journal of Materials Science & Technology 2026年 243卷 149-166页

作者： Guangming Yang Lulu Zeng Hua Shen Huaiyun Cui Tianqi Chen Zengyao Chen Chengwei Xu Chao Liu Feng Huang Zhiyong Liu Zhichao Che Cuiwei Du Xiaogang Li Key Laboratory for Corrosion and Protection (MOE) Institute of Advanced Materials and Technology University of Science and Technology Beijing Beijing 100083 China National Materials Corrosion and Protection Scientific Data Center University of Science and Technology Beijing Beijing 100083 China Jilin Oilfield Company China National Petroleum Corporation Songyuan 138000 China Corrosion and Control Research Center Branch of Science and Technology Research Institute of National Oil and Gas Pipeline Network Group Co Tianjin 300457 China The State Key Laboratory of Refractories and Metallurgy Wuhan University of Science and Technology Wuhan 430081 China School of Metallurgical and Ecological Engineering University of Science and Technology Beijing Beijing 100083 China

This work investigated the effect of dissolved oxygen (DO) on the corrosion behavior and pitting mechanism of X70 pipeline steel in near-neutral soil-bentonite simulated environment. The localized corrosion evolution to uniform corrosion was quantitatively analyzed using statistical methods. In situ characterization reveals that the localized corrosion mechanism is induced by core-shell inclusions. The microcracks occur between MnS and core oxides, the galvanic effect exists between MnS and matrix, and the high distortion region of the matrix promotes the localized corrosion initiation, while the galvanic effect between ferrite and pearlite aids propagation. Interestingly, the pitting growth rates are higher at low DO concentrations. Furthermore, the lower DO and longer immersion time enhance rust layer protection and reduce the corrosion rate of X70 pipeline steel.

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