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Testing a quantum error-correcting code on various platforms

Science Bulletin 2021年第1期66卷 29-35,M0003页

作者： Qihao Guo Yuan-Yuan Zhao Markus Grassl Xinfang Nie Guo-Yong Xiang Tao Xing Zhang-Qi Yin Bei Zeng Institute for Quantum Computing Baidu ResearchBeijing 100193China Department of Applied Physics Xi’an Jiaotong UniversityXi’an 710049China Center for Quantum Computing Peng Cheng LaboratoryShenzhen 518055China CAS Key Laboratory of Quantum Information University of Science and Technology of ChinaHefei 230026China Max Planck Institute for the Science of Light 91058 ErlangenGermany International Centre for Theory of Quantum Technologies 80-308 GdańskPoland Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and TechnologyShenzhen 518055China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements(MOE) School of PhysicsBeijing Institute of TechnologyBeijing 100081China Department of Physics The Hong Kong University of Science and TechnologyHong KongChina.

Quantum error correction plays an important role in fault-tolerant quantum information *** is usually difficult to experimentally realize quantum error correction,as it requires multiple qubits and quantum gates with high *** we propose a simple quantum error-correcting code for the detected amplitude damping *** code requires only two *** implement the encoding,the channel,and the recovery on an optical platform,the IBM Q System,and a nuclear magnetic resonance *** all of these systems,the error correction advantage appears when the damping rate exceeds some *** compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

关键词： Quantum error correction Quantum computation Superconducting circuit NMR system Optical platform

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Higher-order topological in-bulk corner state in pure diffusion systems

arXiv

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arXiv 2022年

作者： Liu, Zhoufei Cao, Pei-Chao Xu, Liujun Xu, Guoqiang Li, Ying Huang, Jiping Department of Physics State Key Laboratory of Surface Physics Key Laboratory of Micro and Nano Photonic Structures MOE Fudan University Shanghai200438 China State Key Laboratory of Extreme Photonics and Instrumentation ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Hangzhou310027 China International Joint Innovation Center Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang The Electromagnetics Academy Zhejiang University Haining314400 China Shaoxing Institute Zhejiang University Shaoxing312000 China Graduate School China Academy of Engineering Physics Beijing100193 China Department of Electrical and Computer Engineering National University of Singapore Kent Ridge 117583 Singapore

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form similarity between Schrödinger equation and diffusion equation, researches on higher-order topological insulators have been extended from condensed matter physics to thermal diffusion. Unfortunately, all the corner states of thermal higher-order topological insulator reside within the band gap. Another kind of corner state, which is embedded in the bulk states, has not been realized in pure diffusion systems so far. Here, we construct higher-dimensional Su-Schrieffer-Heeger models based on sphere-rod structure to elucidate these corner states, which we term "in-bulk corner states". Due to the antiHermitian properties of diffusive Hamiltonian, we investigate the thermal behaviour of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviours of in-bulk corner state and in-gap corner state. Our results would open a different gate for diffusive topological states and provide a distinct application for efficient heat dissipation. © 2022, CC BY.

关键词： Topology

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Boundary stabilization of coupled wave system with spatially-varying coefficients and internal anti-damping

Boundary stabilization of coupled wave system with spatially...

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第三十九届中国控制会议

作者： Xiaodan Feng Zhifei Zhang Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology

In this paper, we consider the exponential stabilization of coupled wave equations with spatially-varying coefficients and internal anti-damping. In contrast to the previous work in the literature, the kernel equations of this system are much more complicated. Using the backstepping method, we verify the kernel equations, which is a system of coupled linear wave equations with spatially-varying coefficients. Then by designing a new characteristic line, the well-posedness of the kernel equations is obtained. Finally we use a Lyapunov function to get the exponential stabilization. A numerical example is presented to illustrate the result.

关键词： backstepping boundary control coupled wave system spatially-varying coefficients

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arXiv

引用

arXiv 2024年

作者： Bang, Jeaheang Gui, Changfeng Liu, Hao Wang, Yun Xie, Chunjing Institute for Theoretical Sciences Westlake University China 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

This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the flux of the flow to guarantee the existence of self-similar solutions of a given type. We also investigate the uniqueness and non-uniqueness of flows with a given type. The non-uniqueness result is a new phenomenon for these flows. Our results not only give rigorous justifications for some statements in [23] but also show that some numerical computations in [23] may not be precise. As a consequence of the classification of self-similar solutions in the half-space, we characterize the leading order term of the steady Navier-Stokes system in an aperture domain when the flux is small. The main approach is to study the ODE system governing self-similar solutions, where the detailed properties of both complete and incomplete elliptic functions have been investigated. Copyright © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

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New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

arXiv

引用

arXiv 2020年

作者： Zhao, Ting Liu, Hongwei Liu, Zexian School of Mathematics and Statistics Xidian University Xi’an710126 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing100190 China

In this paper, two new subspace minimization conjugate gradient methods based on p−regularization models are proposed, where a special scaled norm in p−regularization model is analyzed. Different choices for special scaled norm lead to different solutions to the p−regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R−linear convergence of the proposed methods are also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J Optim 16(1):170-192, 2005), Dai and Kou (SIAM J Optim 23(1):296-320, 2013), Liu and Liu (J Optim Theory Appl 180(3):879-906, 2019) and Li et al. (Comput Appl Math 38(1): 2019), respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： Conjugate gradient method

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CDOpt: A Python Package for a Class of Riemannian Optimization

arXiv

引用

arXiv 2022年

作者： Xiao, Nachuan Hu, Xiaoyin Liu, Xin Toh, Kim-Chuan The Institute of Operations Research and Analytics National University of Singapore Singapore School of Computer and Computing Science Hangzhou City University Hangzhou China Academy of Edge Intelligence Hangzhou City University Gongshu Hangzhou China 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 Singapore

Optimization over an embedded submanifold defined by equality constraints c(x) = 0 has attracted much interest over the past few decades due to its wide applications in various areas, including computer vision, signal processing, numerical linear algebra, and deep learning. For solving such problems, many related optimization packages have been developed based on Riemannian optimization approaches, which rely on some basic geometrical materials of Riemannian manifolds, including Riemannian gradients, retractions, vector transports, etc. These geometrical materials can be challenging to determine in general. In fact, existing packages only accommodate a few well-known manifolds whose geometrical materials are more easily accessible. For other manifolds that are not contained in these packages, the users have to develop the geometric materials by themselves. In addition, it is not always tractable to adapt the advanced features from various state-of-the-art unconstrained optimization solvers to Riemannian optimization approaches. Here we introduce a user-friendly Python package, CDOpt (available at https: //***/ under BSD 3-clause license), for solving a class of Riemannian optimization problems. CDOpt is designed to complement existing Riemannian optimization packages by transforming Riemannian optimization problems into their unconstrained counterparts through the constraint dissolving approach. We prove that the when the penalty parameter in the constraint dissolving approach is sufficiently large, Riemannian optimization problems and their unconstrained counterparts are equivalent. Therefore, solving Riemannian optimization problems through CDOpt can directly benefit from various existing solvers and the rich expertise gained over the past few decades for unconstrained optimization. Moreover, all the computations in CDOpt related to any manifold in question are conducted through its constraints expression, hence users can easily define new manifolds in

关键词： Constrained optimization

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Influence of Small-Size Contaminations on Thin Film Structural Properties

引用

Chinese Physics Letters 2019年第3期36卷 82-85页

作者： F.V.Grigoriev V.B.Sulimov Jinlong Zhang Xinbin Cheng Zhanshan Wang A.V.Tikhonravov Research Computing Center M.V.Lomonosov Moscow State University MOE Key Laboratory of Advanced Micro-Structured Materials Institute of Precision Optical Engineering School of Physics Science and EngineeringTongji University IFSA Collaborative Innovation Center Shanghai Jiao Tong University

An approach for studying the influence of nano-particles on the structural properties of deposited thin films is proposed. It is based on the molecular dynamic modeling of the deposition process in the presence of contaminating nano-particles. The nano-particle is assumed to be immobile and its interaction with film atoms is described by a spherically symmetric potential. The approach is applied to the investigation of properties of silicon dioxide films. Visualization tools are used to investigate the porosity associated with nano-particles. The structure of the film near the nano-particle is studied using the radial distribution function. It is found that fluctuations of film density near the nano-particles are essentially different in the cases of low-energy and high-energy deposition processes.

关键词： Influence Small-Size Properties

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Quantum algorithms for computing observables of nonlinear partial differential equations

arXiv

引用

arXiv 2022年

作者： Jin, Shi Liu, Nana Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China School of Mathematical 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

We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear Hamilton-Jacobi and scalar hyperbolic PDEs can be performed with a computational cost that is independent of M, for arbitrary nonlinearity. Depending on the details of the initial data, it can also display up to exponential advantage in both the dimension of the PDE and the error in computing its observables. For general nonlinear PDEs, quantum advantage with respect to M is possible in the large M limit. © 2022, CC BY.

关键词： Quantum theory

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LIOUVILLE-TYPE THEOREMS FOR STEADY SOLUTIONS TO THE NAVIER-STOKES SYSTEM IN A SLAB

arXiv

引用

arXiv 2022年

作者： Bang, Jeaheang Gui, Changfeng Wang, Yun Xie, Chunjing Department of Mathematics The University of Texas San Antonio United States 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

Liouville-type theorems for the steady incompressible Navier-Stokes system are investigated for solutions in a three-dimensional slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary conditions are prescribed, we prove that any bounded solution is trivial if it is axisymmetric or rur is bounded, and that general three-dimensional solutions must be Poiseuille flows when the velocity is not big in L∞ space. When the periodic boundary conditions are imposed on the slab boundaries, we prove that the bounded solutions must be constant vectors if either the swirl or radial velocity is independent of the angular variable, or rur decays to zero as r tends to infinity. The proofs are based on the fundamental structure of the equations and energy estimates. The key technique is to establish a Saint-Venant type estimate that characterizes the growth of Dirichlet integral of nontrivial solutions. Copyright © 2022, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Convergence analysis of one-point large deviations rate functions of numerical discretizations for stochastic wave equations with small noise

arXiv

引用

arXiv 2022年

作者： Jin, Diancong Hong, Jialin Sheng, Derui School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this work, we present the convergence analysis of one-point large deviations rate functions (LDRFs) of the spatial finite difference method (FDM) for stochastic wave equations with small noise, which is essentially about the asymptotical limit of minimization problems and not a trivial task for the nonlinear cases. In order to overcome the difficulty that objective functions for the original equation and the spatial FDM have different effective domains, we propose a new technical route for analyzing the pointwise convergence of the one-point LDRFs of the spatial FDM, based on the Γ -convergence of objective functions. Based on the new technical route, the intractable convergence analysis of one-point LDRFs boils down to the qualitative analysis of skeleton equations of the original equation and its numerical discretizations. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method

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