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.

最近的尖端和近距离量子设备将以探测新的物理领域并增强对物理学的基础理解的方式来推动信息处理，计算和测量中信息处理的界限。该项目研究了为这些革命性技术的“量子优势”供电的量子纠缠和其他非本地特性。 PI试图为量子计算机和量子通信网络设计有用的应用程序。除了通过新的结果实现科学进步外，一个主要的项目组成部分是通过参与实际研究的科学发展。本项目将实施一个系统的框架，研究多体状态的本地统一和置换式对称性，以探测多Artiparticle量子量子纠缠并开发量子协议的应用。纠缠分析的主要工具是使用本地操作组的各向同性亚组（即留下给定状态不变的一单位者）；这些各向同性组的同构类是纠缠不变的，不仅可以用于分类，而且还用于设计算法和协议。方法论包括谎言群体和谎言代数的理论，代表理论和Schur-weyl二元性，以及提案者的过去结果。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛的影响来通过评估来支持的。

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