CIF: Small: Learning Quantum Information Measures

CIF：小：学习量子信息测量

基本信息

批准号：
1815893
负责人：
Jayadev Acharya
金额：
$ 48.8万
依托单位：
Cornell University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-10-01 至 2022-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815893&HistoricalAwards=false
关键词：
CIF Small Learning Quantum Information

项目摘要

Quantum information processing systems are becoming practical with the expectation that these systems will soon be commercialized within a decade, and will be a part of our everyday life. However, our understanding of the amount of information that can be gleaned from a quantum system is still very rudimentary. For example, the complexity of the basic question of learning a quantum state (called tomography) was only resolved in the past few years, whereas its classical analogue of distribution estimation is now textbook material in any introductory statistics course. Research under this award will be dedicated to the study of the problem of estimating fundamental information measures, as well as introduce new information measures for quantum systems. The project will establish the fundamental limits of the information processing capabilities of quantum information systems, as well as design novel algorithms that can match these limits. The project outcomes can enable the development of efficient quantum computer and communication systems.The award will develop a deeper understanding of a quantum system as a statistical mechanism, and integrate ideas from various disciplines such as representation theory, information theory, statistics, and computer science. A novel variation of the statistical principle of maximum likelihood estimation as a general methodology for quantum property estimation will be proposed and developed. The project will also study the extension of representation theory results of Schur-Weyl duality to higher dimensions to obtain optimal quantum measurement schemes for properties of multiple quantum systems. The work includes proposing measurement schemes that are more realistic than the theoretically-optimal ones considered in the literature that in practice are too complex to be implemented with existing technology.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.

量子信息处理系统正在变得实用，预计这些系统将在十年内很快实现商业化，并成为我们日常生活的一部分。然而，我们对可以从量子系统收集的信息量的理解仍然非常初级。例如，学习量子态（称为断层扫描）这一基本问题的复杂性在过去几年才得到解决，而其经典的分布估计类似物现在已成为任何统计入门课程的教科书材料。该奖项的研究将致力于研究估计基本信息度量的问题，并为量子系统引入新的信息度量。该项目将确定量子信息系统信息处理能力的基本限制，并设计能够匹配这些限制的新颖算法。该项目成果可以促进高效量子计算机和通信系统的开发。该奖项将加深对量子系统作为统计机制的理解，并整合表示论、信息论、统计学和计算机科学等不同学科的思想。将提出并开发最大似然估计统计原理的一种新颖变体，作为量子特性估计的通用方法。该项目还将研究将Schur-Weyl对偶性的表示论结果扩展到更高维度，以获得多量子系统特性的最佳量子测量方案。这项工作包括提出比文献中考虑的理论上最佳方案更现实的测量方案，而在实践中，这些方案过于复杂，无法用现有技术来实施。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。