CQIS: RUI: Quantum State Symmetry and Applications

CQIS：RUI：量子态对称性及其应用

• 批准号: 2011074
• 负责人: David Lyons
• 金额: $ 21.04万
• 依托单位: Lebanon Valley College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2011074&HistoricalAwards=false
• 关键词: CQIS; RUI; Quantum; State; Symmetry

Recent cutting-edge and near-future quantum devices will push the boundaries of information processing in communication, computation, and measurement in ways that will probe new physical realms and enhance the foundational understanding of physics. This project studies quantum entanglement and other nonlocal properties that power the "quantum advantage" of these revolutionary technologies. The PI seeks to design useful applications for quantum computers and quantum communication networks. In addition to achieving scientific progress through new results, a major project component is scientific development of undergraduate students through participation in real research.This project will implement a systematic framework studying local unitary and permutational symmetries of many-body states to probe multiparticle quantum entanglement and to develop applications for quantum protocols. A main tool for entanglement analysis is the use of isotropy subgroups (that is, the set of unitaries that leave a given state invariant) of the group of local operations; the isomorphism classes of these isotropy groups are entanglement invariants that can be used not only for classification, but also for designing algorithms and protocols. Methodology includes the theory of Lie groups and Lie algebras, representation theory and Schur-Weyl duality, together with the proposer's past results.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.

最近的尖端和不久的将来的量子设备将以探索新的物理领域和增强对物理学的基础理解的方式，在通信、计算和测量方面推动信息处理的边界。这个项目研究量子纠缠和其他非局域特性，这些特性为这些革命性技术的“量子优势”提供动力。PI寻求为量子计算机和量子通信网络设计有用的应用程序。除了通过新的成果实现科学进步外，一个主要的项目组成部分是通过参与实际研究来促进本科生的科学发展。该项目将实施一个系统框架，研究多体状态的局域么正对称性和置换对称性，以探索多粒子量子纠缠，并开发量子协议的应用。纠缠分析的一个主要工具是使用局部运算群的各向同性子群(即，保持给定状态不变的酉集)；这些各向同性群的同构类是纠缠不变量，不仅可用于分类，还可用于设计算法和协议。方法论包括李群和李代数理论、表示理论和Schur-Weyl对偶理论，以及提名者过去的结果。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Werner states from diagrams

• DOI: 10.1088/1751-8121/acd039
• 发表时间: 2023-02
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: David W. Lyons;C. Mullican;Adam Rilatt;Jack D. Putnam

Local unitary classes of states invariant under permutation subgroups

置换子群下不变的局部酉态类

• DOI: 10.1103/physreva.105.032442
• 发表时间: 2022
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Lyons, David W.;Arnold, Jesse R.;Swogger, Ashley F.
• 通讯作者: Swogger, Ashley F.

Finite-Function-Encoding Quantum States

• DOI: 10.22331/q-2022-05-09-708
• 发表时间: 2020-12
• 期刊: Quantum
• 影响因子: 6.4
• 作者: Paul Appel;Alexander J. Heilman;E. W. Wertz;David W. Lyons;M. Huber;Matej Pivoluska;G. Vitagliano