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Efficient learning of continuous-variable quantum states

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Physical Review Research 2024年第3期6卷 033280页

作者： Ya-Dong Wu Yan Zhu Giulio Chiribella Nana Liu John Hopcroft Center for Computer Science QICI Quantum Information and Computation Initiative Department of Computer Science The Department of Computer Science for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Institute of Natural Sciences Ministry of Education Key Laboratory in Scientific and Engineering Computing School of Mathematical Sciences University of Michigan-

The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation, and computing. However, a full characterization of multimode quantum states requires a number of experiments that grows exponentially with the number of modes. Here we propose an alternative approach where the goal is not to reconstruct the full quantum state, but rather to estimate its characteristic function at a given set of points. For multimode states with reflection symmetry, we show that the characteristic function at M points can be estimated using only O(logM) copies of the state, independently of the number of modes. When the characteristic function is known to be positive, as in the case of squeezed vacuum states, the estimation is achieved by an experimentally friendly setup using only beamsplitters and homodyne measurements.

关键词： Machine learning Quantum information processing with continuous variables Quantum tomography

Efficient explicit circuit for quantum state preparation of piece-wise continuous functions

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arXiv 2024年

作者： Guseynov, Nikita Liu, Nana University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai200240 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 Shanghai Artificial Intelligence Laboratory Shanghai China

The ability to effectively upload data onto quantum states is an important task with broad applications in quantum computing. Numerous quantum algorithms heavily rely on the ability to efficiently upload information onto quantum states, without which those algorithms cannot achieve quantum advantage. In this paper, we address this challenge by proposing a method to upload a polynomial function f(x) on the interval x ∈ (a,b) onto a pure quantum state consisting of qubits, where a discretised f(x) is the amplitude of this state. The preparation cost has quadratic scaling in the number of qubits n and linear scaling with the degree of the polynomial Q. This efficiency allows the preparation of states whose amplitudes correspond to high-degree polynomials, enabling the approximation of almost any continuous function. We introduce an explicit algorithm for uploading such functions using four real polynomials that meet specific parity and boundedness conditions. We also generalize this approach to piece-wise polynomial functions, with the algorithm scaling linearly with the number of piecewise parts. Our method achieves efficient quantum circuit implementation and we present detailed gate counting and resource *** Codes 68Q12 © 2024, CC BY.

关键词： Qubits

A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold

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arXiv 2021年

作者： Xiao, Nachuan Liu, Xin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and 2,1-norm regularized cases, these infeasible approaches adopt simple and orthonormalizationfree updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final solution, these infeasible approaches introduce a quadratic penalty term,where an inappropriate penalty parameter can lead to numerical inefficiency. Inspired by penalty-free approaches for smooth optimization problems, we proposed a sequential linearized proximal gradient method (SLPG) for a class of optimization problems with orthogonality constraints and nonsmooth regularization term. This approach alternatively takes tangential steps and normal steps to improve the optimality and feasibility respectively. In SLPG, the orthonormalization process is invoked only once at the last step if high precision for feasibility is needed, showing that main iterations in SLPG are orthonormalization-free. Besides, both the tangential steps and normal steps do not involve the penalty parameter, and thus SLPG is penaltyfree and avoids the inefficiency caused by possible inappropriate penalty parameter. We analyze the global convergence properties of SLPG where the tangential steps are inexactly computed. By inexactly computing tangential steps, for smooth cases and 2,1-norm regularized cases, SLPG has a closed-form updating scheme, which leads to cheap tangential steps. Numerical experiments illustrate the advantages of SLPG when compared with existing first-ordermethods. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

Research on patent recommendation method based on graph neural network

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Research on patent recommendation method based on graph neur...

International Conference on Computer Supported Cooperative Work in Design

作者： Enchao Zhang Weidong Liu Shi Liu Yan Cao College of Computer Science Inner Mongolia University China Institute of Scientific and Technical Information of China China National & Local Joint Engineering Research Center of Intelligent Information Processing Technology for Mongolian China Inner Mongolia Key Laboratory of Social Computing and Data Processing China Inner Mongolia Engineering Laboratory for Big Data Analysis Technology China

Intellectual property transactions have shown a strong growth momentum in recent years, but the patent transaction market has been plagued by the matching degree of consumers and sellers, resulting in frequent problems such as low patent transformation efficiency and poor transaction quality. This paper proposes a method of recommending patents to consumers by experts to improve the environment of patent transactions. Through the analysis of the past transaction information of the patent, the effective path information of the target is extracted. The graph neural network is used to describe the characteristics and semantics among experts, patents and consumers, and then capture the potential weight among them through the common attention mechanism, and then dynamically integrate them to predict the occurrence of recommendation behavior. The paper makes reasonable use of social information and expert information in the transaction, which significantly improves the rationality and accuracy of expert recommendation.

关键词：

THE QUADRATIC SPECHT TRIANGLE

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Journal of Computational Mathematics 2020年第1期38卷 103-124页

作者： Hongliang Li Pingbing Ming Zhongci Shi Department of Mathematics Sichuan Normal UniversityChengdu 610066China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesNo.55East Road ZhongGuanCunBeijing 100190China

We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of *** may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending *** convergence result is proved under minimal smoothness assumption on the *** results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.

关键词： Specht triangle Plate bending element Basis functions

Learning-rate-free Momentum SGD with Reshuffling Converges in Nonsmooth Nonconvex Optimization

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arXiv 2024年

作者： Hu, Xiaoyin Xiao, Nachuan Liu, Xin Toh, Kim-Chuan School of Computer and Computing Science Hangzhou City University Hangzhou310015 China Institute of Operational Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China Department of Mathematics Institute of Operations Research and Analytics National University of Singapore Singapore119076 Singapore

In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex functions, especially in training nonsmooth neural networks. Our framework adaptively generates learning rates based on the historical data of stochastic subgradients and iterates. Under mild conditions, we prove that our proposed framework enjoys global convergence to the stationary points of the objective function in the sense of the conservative field, hence providing convergence guarantees for training nonsmooth neural networks. Based on our proposed framework, we propose a novel learning-rate-free momentum SGD method (LFM). Preliminary numerical experiments reveal that LFM performs comparably to the state-of-the-art learning-rate-free methods (which have not been shown theoretically to be convergence) across well-known neural network training benchmarks. Copyright © 2024, The Authors. All rights reserved.

关键词： Momentum

Exploring Patent Transformation Event: Forecasting Patent Transfer Time

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Exploring Patent Transformation Event: Forecasting Patent Tr...

International Conference on Computer Supported Cooperative Work in Design

作者： Jinchen Huo Weidong Liu Yang Li Yan Cao College of Computer Science Inner Mongolia University China Institute of Scientific and Technical Information of China China National & Local Joint Engineering Research Center of Intelligent Information Processing Technology for Mongolian China Inner Mongolia Key Laboratory of Social Computing and Data Processing China Inner Mongolia Engineering Laboratory for Big Data Analysis Technology China

As the largest source of technical information around the world, patents are regarded as an essential crystallization and carrier of knowledge and technological innovation. Patent transformation is conducive not only to enhancing economic efficiency, but also to improving productivity and the rational utilization of resources. There is an imbalance between high patent ownership and low transformation rates. We try to predict the occurrence of transformation events from the patent assignment. However, there are some challenges in predicting patent transformation: (1) how to capture transformation features of patents, especially combined with the transfer time factor. (2) how to predict patent transfer time effectively. To address these challenges, a Patent Transfer Time Forecasting Model (PTTFM) is proposed. The model includes: (1) extraction of time-varying features of patents. (2) the patent transfer time is forecast using a Neural Temporal Point Process. By testing the model on patents under different classifications, the experimental results are obtained to show that the proposed model is applicable to predict the timing of patent assignment within a certain time frame, especially one month. Our work may facilitate patent transformation while interpretability is ensured for transformation events.

关键词：

Pseudo complementary measurement for traditional single-pixel cameras

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Chinese Physics B 2020年第11期29卷 315-322页

作者： Qian Dong Xu-Ri Yao Xin Liu Bing Liu Guang-Jie Zhai State Key Laboratory of Computer Science Institute of SoftwareChinese Academy of SciencesBeijing 100190China Key Laboratory of Electronics and Information Technology for Space Systems National Space Science CenterChinese Academy of SciencesBeijing 100190China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing *** with the 1/0 matrices in classical measurement,the 1/-1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction ***,each row of the 1/-1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 *** this paper,we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/-1 matrix in a mathematical *** numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate,which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.

关键词： computational imaging single-pixel camera

Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation

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arXiv 2022年

作者： Cao, Liyuan Wen, Zaiwen Yuan, Ya-Xiang Beijing International Center for Mathematical Research Peking University Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the function has Lipschitz continuous gradient and is interpolated on an affinely independent sample set. Errors for quadratic functions and errors of bivariate linear extrapolation are analyzed in *** Codes 41A05, 41A10, 41A80, 46N10 Copyright © 2022, The Authors. All rights reserved.

关键词： Extrapolation