From Quantum Entanglement to Tensor Decomposition by Global Optimization

从量子纠缠到全局优化的张量分解

基本信息

批准号：
1912816
负责人：
Moody Chu
金额：
$ 47.08万
依托单位：
North Carolina State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912816&HistoricalAwards=false
关键词：
Quantum Entanglement Tensor Decomposition Global

项目摘要

Entanglement and separability are twins. Entanglement is the most basic mode when characterizing the coupling or interaction of multiple parts within a system; separability is to represent the complicated system in an equivalent but more manifesting relationship for understanding and control. This project aims to develop methods to numerically measure the "absolute" gap between an entangled state and its nearest separable state with the new tool of global optimization techniques. The initial goal is to establish a basal paradigm for gauging entanglement and separability with global optimization technologies in the context of quantum informatics. With modest modification, the paradigm can be applied across different fields. Results from this research will make it possible to address separability issues in many other contexts, such as economic development, agricultural production, industrial manufacture, environmental evolution, social networks, and applied mechanics, where constituents, factors, parts, or subsystems are regularly intertwined.Quantum entanglement is regarded as an indispensable resource for many applications due to the potential of quantum computing for fast, concurrent computation. The nonlinear correlations among subsystems make it difficult to analyze by traditional decomposition techniques. On the other hand, the notion of tensors has also gained new attention thanks to its great descriptive flexibility. Both structures share similar features concerning entanglement and separability. There have been many activities and achievements on both fronts. Yet, the avenue of numerically measuring the "absolute" gap between an entangled state and its nearest separable state has never been fully undertaken. This project aims to tackle both quantum entanglement and low-rank tensor approximation under one framework by global optimization techniques. When global optimization is finished, within the prescribed error tolerance we have in hand the metric between a given state and the set of separable states, by which we can gauge the quality of entanglement, draw conclusions on whether the given system is robustly entangled, and extend the knowledge to other applications. This project aims to establish theoretic and algorithmic foundations to: 1) exploit the geometric properties of entanglement; 2) develop a common platform for new algorithms effective in robustness, speed, and accuracy; and 3) explore the generalization to applications with additional constraints. This research together with the resulting software package is expected to find wide applicability extending from quantum mechanics to data analysis, network analysis, and other fields. The work will solidify study of many features under one unified framework.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

纠缠和分离是双胞胎。纠缠是表征系统内多个部分的耦合或相互作用时最基本的模式；可分离性就是用一种等价但更明显的关系来表示复杂的系统，以便于理解和控制。该项目旨在开发方法，利用全局优化技术的新工具，对纠缠态与其最近的可分离态之间的“绝对”差距进行数值测量。最初的目标是建立一个基本范式，用于在量子信息学背景下用全局优化技术来衡量纠缠和可分离性。通过适当的修改，该范式可以应用于不同的领域。这项研究的结果将使得解决许多其他背景下的可分离性问题成为可能，例如经济发展、农业生产、工业制造、环境演变、社会网络和应用力学，其中成分、因素、零件或子系统经常交织在一起由于量子计算在快速、并发计算方面的潜力，量子纠缠被认为是许多应用中不可或缺的资源。子系统之间的非线性相关性使得传统的分解技术难以进行分析。另一方面，张量的概念由于其极大的描述灵活性也获得了新的关注。两种结构在纠缠和可分离性方面具有相似的特征。在这两个方面都开展了许多活动并取得了成果。然而，数值测量纠缠态与其最近的可分离态之间“绝对”间隙的途径从未被完全采用。该项目旨在通过全局优化技术在一个框架下解决量子纠缠和低秩张量近似。当全局优化完成后，在规定的误差容限内，我们掌握了给定状态和可分离状态集之间的度量，通过它我们可以衡量纠缠的质量，得出给定系统是否鲁棒纠缠的结论，以及将知识扩展到其他应用程序。该项目旨在建立理论和算法基础，以：1）利用纠缠的几何特性； 2) 为在稳健性、速度和准确性方面有效的新算法开发通用平台； 3）探索对具有附加约束的应用程序的泛化。这项研究以及由此产生的软件包预计将具有从量子力学扩展到数据分析、网络分析和其他领域的广泛适用性。这项工作将在一个统一的框架下巩固对许多特征的研究。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。