检索结果-内蒙古大学图书馆

semidefinite program for One-Shot Dilution of Quantum Coherence

ADVANCED QUANTUM TECHNOLOGIES 2024年第0期

作者： Zhu, Yikang Su, Zhaofeng Univ Sci & Technol China Sch Comp Sci & Technol Hefei 230026 Peoples R China Univ Sci & Technol China CAS Key Lab Wireless Opt Commun Hefei 230026 Peoples R China

Quantum coherence is one of the fundamental properties of quantum mechanics and also acts as a valuable resource for a variety of practical applications, which includes quantum computing and quantum information processing. Evaluating the dilution of coherence is a basic problem in the framework of resource theory. The coherence dilution problem is considered in the one-shot scenario. A semidefinite program of one-shot coherence dilution of pure state under maximally incoherent operation is identified. A similar but not semidefinite program form is provided under dephasing-covariant incoherent operation. Moreover, it is proved that the known lower bound of the one-shot dilution is strict. This numerical experiment clearly demonstrates that the maximally incoherent operation and dephasing-covariant incoherent operation have different power in the coherence dilution.

关键词： one-shot dilution quantum coherence semidefinite program

来源：评论

学校读者我要写书评

暂无评论

Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space

引用

JOURNAL OF GLOBAL OPTIMIZATION 2022年第2期84卷 415-440页

作者： Zheng, Meng-Meng Huang, Zheng-Hai Hu, Sheng-Long Natl Univ Def Technol Dept Math Changsha 410073 Hunan Peoples R China Tianjin Univ Sch Math Tianjin 300350 Peoples R China Hangzhou Dianzi Univ Sch Sci Dept Math Hangzhou 310018 Peoples R China

In this paper, unconstrained minimization with block-circulant structured polynomials is studied. A specifically designed method is presented to show that it can solve problems with sizes much larger than the classical Lasserre's semidefinite relaxation. The proposed approach is in the same spirit of Lasserre's relaxation but with a careful exploration of the underlying circulant structure, which helps reducing the sizes of the result semidefinite program problems significantly. Despite of the reduction, a certification for the global optimality is derived as well.

关键词： Unconstrained polynomial optimization problem Block-circulant structure Lasserre's relaxation semidefinite program

来源：评论

学校读者我要写书评

暂无评论

A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test

引用

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2018年第1期25卷 n/a-1页

作者： Chen, Haibin Chen, Yannan Li, Guoyin Qi, Liqun Qufu Normal Univ Sch Management Sci Rizhao Peoples R China Zhengzhou Univ Sch Math & Stat Zhengzhou Henan Peoples R China Univ New South Wales Dept Appl Math Sydney NSW Australia Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. In this paper, we introduce a new class of structured tensors called W-tensors, which not only extends the well-studied nonnegative tensors by allowing negative entries but also covers several important tensors arising naturally from spectral hypergraph theory. We then show that finding the maximum H-eigenvalue of an even-order symmetric W-tensor is equivalent to solving a structured semidefinite program and hence can be validated in polynomial time. This yields a highly efficient semidefinite program algorithm for computing the maximum H-eigenvalue of W-tensors and is based on a new structured sums-of-squares decomposition result for a nonnegative polynomial induced by W-tensors. Numerical experiments illustrate that the proposed algorithm can successfully find the maximum H-eigenvalue of W-tensors with dimension up to 10,000, subject to machine precision. As applications, we provide a polynomial time algorithm for computing the maximum H-eigenvalues of large-size Laplacian tensors of hyperstars and hypertrees, where the algorithm can be up to 13 times faster than the state-of-the-art numerical method introduced by Ng, Qi, and Zhou in 2009. Finally, we also show that the proposed algorithm can be used to test the copositivity of a multivariate form associated with symmetric extended Z-tensors, whose order may be even or odd.

关键词： copositivity eigenvalues Laplacian tensor semidefinite program spectral hypergraph structured tensors sum-of-squares polynomials

来源：评论

学校读者我要写书评

暂无评论

semidefinite programming Bounds on the Size of Entanglement-Assisted Codeword Stabilized Quantum Codes

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第11期70卷 7867-7881页

作者： Lai, Ching-Yi Tseng, Pin-Chieh Yu, Wei-Hsuan Natl Yang Ming Chiao Tung Univ NYCU Inst Commun Engn Hsinchu 30010 Taiwan Natl Yang Ming Chiao Tung Univ NYCU Dept Appl Math Hsinchu 30010 Taiwan Natl Cent Univ Dept Math Taoyuan 32001 Taiwan

In this paper, we explore the application of semidefinite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the CWS group and the set of word operators of a CWS-type quantum code to derive an upper bound on the minimum distance. Furthermore, this characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints that lead to SDP bounds on the minimum distance or size of CWS-type quantum codes. We illustrate several instances where SDP bounds outperform LP bounds, and there are even cases where LP fails to yield meaningful results, while SDP consistently provides tighter and relevant bounds. Finally, we also provide interpretations of the Shor-Laflamme weight enumerators and shadow enumerators for codeword stabilized codes, enhancing our understanding of quantum codes.

关键词： Codes Vectors Upper bound Quantum entanglement Algebra programming Error correction codes Quantum codes codeword stabilized (CWS) codes semidefinite program Terwilliger algebra weight enumerator

来源：评论

学校读者我要写书评

暂无评论

semidefinite programming bounds for binary codes from a split Terwilliger algebra

引用

DESIGNS CODES AND CRYPTOGRAPHY 2023年第10期91卷 3241-3262页

作者： Tseng, Pin-Chieh Lai, Ching-Yi Yu, Wei-Hsuan Natl Yang Ming Chiao Tung Univ Inst Commun Engn Hsinchu 30010 Taiwan Natl Yang Ming Chiao Tung Univ Dept Appl Math Hsinchu 30010 Taiwan Natl Cent Univ Dept Math Taoyuan 32001 Taiwan

We study the upper bounds for A(n, d), the maximum size of codewords with length n and Hamming distance at least d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound A(n, d). We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver's semidefinite programming bounds on A(n, d). In particular, we improve the semidefinite programming bounds on A(18, 4) to 6551.

关键词： semidefinite program Binary codes Terwilliger algebra Weight enumeration Distance distribution

来源：评论

学校读者我要写书评

暂无评论

Accelerated first-order methods for a class of semidefinite programs

引用

MATHEMATICAL programMING 2025年第1-2期209卷 503-556页

作者： Wang, Alex L. Kilinc-Karzan, Fatma Carnegie Mellon Univ Pittsburgh PA 15213 USA Purdue Univ W Lafayette IN 47907 USA

This paper introduces a new storage-optimal first-order method, CertSDP, for solving a special class of semidefinite programs (SDPs) to high accuracy. The class of SDPs that we consider, the exact QMP-like SDPs, is characterized by low-rank solutions, a priori knowledge of the restriction of the SDP solution to a small subspace, and standard regularity assumptions such as strict complementarity. Crucially, we show how to use a certificate of strict complementarity to construct a low-dimensional strongly convex minimax problem whose optimizer coincides with a factorization of the SDP optimizer. From an algorithmic standpoint, we show how to construct the necessary certificate and how to solve the minimax problem efficiently. Our algorithms for strongly convex minimax problems with inexact prox maps may be of independent interest. We accompany our theoretical results with preliminary numerical experiments suggesting that CertSDP significantly outperforms current state-of-the-art methods on large sparse exact QMP-like SDPs.

关键词： semidefinite program First-order method Exact Quadratic matrix program Optimal storage

来源：评论

学校读者我要写书评

暂无评论

Improved semidefinite programming bounds for binary codes by split distance enumerations

Improved semidefinite programming bounds for binary codes by...

引用

IEEE International Symposium on Information Theory (ISIT)

ISBN: (纸本)9781665421607;9781665421591

We study the maximum size of a binary code A(n, d) with code length n and minimum distance d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to upper bound A(n, d). We derive additional semidefinite constraints based on a split Terwilliger algebra so that Schrijver's semidefinite programming bounds on A(n, d) can be improved. In particular, we show that A(18, 4) <= 6551 and A(19, 4) <= 13087.

关键词： semidefinite program binary codes Terwilliger algebra

来源：评论

学校读者我要写书评

暂无评论

Improving the Performance of MIQP Solvers for Quadratic programs with Cardinality and Minimum Threshold Constraints: A semidefinite program Approach

引用

INFORMS JOURNAL ON COMPUTING 2014年第4期26卷 690-703页

作者： Zheng, Xiaojin Sun, Xiaoling Li, Duan Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Fudan Univ Sch Management Dept Management Sci Shanghai 200433 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

We consider in this paper quadratic programming problems with cardinality and minimum threshold constraints that arise naturally in various real-world applications such as portfolio selection and subset selection in regression. This class of problems can be formulated as mixed-integer 0-1 quadratic programs. We propose a new semidefinite program (SDP) approach for computing the "best" diagonal decomposition that gives the tightest continuous relaxation of the perspective reformulation of the problem. We also give an alternative way of deriving the perspective reformulation by applying a special Lagrangian decomposition scheme to the diagonal decomposition of the problem. This derivation can be viewed as a "dual" method to the convexification method employing the perspective function on semicontinuous variables. Computational results show that the proposed SDP approach can be advantageous for improving the performance of mixed-integer quadratic programming solvers when applied to the perspective reformulations of the problem.

关键词： quadratic programming with semicontinuous variables and cardinality constraint perspective reformulation diagonal decomposition semidefinite program Lagrangian decomposition

来源：评论

学校读者我要写书评

暂无评论

All saddle points for polynomial optimization

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2025年第3期90卷 721-752页

作者： Zhou, Anwa Yin, Shiqian Fan, Jinyan Shanghai Univ Dept Math Shanghai 200444 Peoples R China Shanghai Jiao Tong Univ Sch Math Sci LSC MOE Shanghai 200240 Peoples R China

In this paper, we study how to compute all saddle points for the constrained and unconstrained polynomial optimization, respectively. For the constrained polynomial optimization, a scalar-type semidefinite relaxation algorithm is proposed based on the Karush-Kuhn-Tucker conditions. While for the unconstrained polynomial optimization, a matrix-type semidefinite relaxation algorithm is proposed based on the second-order optimality conditions. Both algorithms can detect the nonexistence of saddle points or find all of them if there are finitely many ones. The finite convergence of the algorithms can also be obtained under some genericity conditions.

关键词： Saddle points Polynomial optimization Lasserre relaxation semidefinite program Finite convergence

来源：评论

学校读者我要写书评

暂无评论

Data-driven discovery of invariant measures

引用

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2024年第2286期480卷

作者： Bramburger, Jason J. Fantuzzi, Giovanni Concordia Univ Dept Math & Stat Montreal PQ Canada Friedrich Alexander Univ Erlangen Nurnberg Dept Math Erlangen Germany

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and stochastic dynamics in either continuous or discrete time. We provide convergence results and illustrate the performance of our method on data from the logistic map and a stochastic double-well system, for which invariant measures can be found by other means. We then use our method to approximate the physical measure of the chaotic attractor of the Rossler system, and we extract unstable periodic orbits embedded in this attractor by identifying discrete-time periodic points of a suitably defined Poincare map. This final example is truly data-driven and shows that our method can significantly outperform previous approaches based on model identification.

关键词： invariant measure ergodic theory semidefinite program Koopman operator Perron-Frobenius operator Poincare map periodic orbit

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：