FET: Small: Efficient Inference Tools for Quantum Systems: Algorithms, Applications, and Analysis

量子信息科学已经进入了一个令人兴奋的新时代。研究人员现在正积极尝试构建量子计算机，它可以比经典计算机获得显着的收益。例如，肖尔的量子算法分解大整数可以实现指数加速超过目前最好的经典方法。然而，为了实现这一目标，研究人员必须设计容错协议来处理量子现象的脆弱性。在这个更广泛的背景下，该项目将设计有效的协议，从嘈杂的量子设备中提取可靠的信息。该项目的另一部分将使用信息理论工具来研究量子网络的信息处理能力。这些结果有望在量子信息科学中得到广泛的应用。PI还将指导研究生并提供量子技术的本科生研究机会。区分量子态的能力是量子通信和量子信息科学的重要组成部分。即使在相对简单的量子系统中，也很难设计和实现用于量子态鉴别的良好协议。这个项目的一个目标是回答这个问题：是否有有效的方法来区分量子态，适用于大类的实际相关的状态？这与该项目的另一部分有关，该项目的目标是了解量子技术在嘈杂的中等规模量子设备时代的优势和局限性。该项目将研究噪声量子网络中信息和纠缠衰减的速率。例如，我们将推导出噪声阈值，低于该阈值，信息和纠缠可以通过网络传播。这些结果可以应用于容错量子计算，也可以用于分析混沌量子系统（如黑洞）中的信息置乱。该项目中的许多研究方向都建立在分析量子系统的数学工具之上，例如强数据处理不等式。该项目的最后一部分将开发这些工具，并推导出量子态鉴别和量子网络的信息理论极限。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum information science has entered an exciting new era. Researchers are now actively trying to build quantum computers that can achieve significant gains over classical computers. For example, Shor's quantum algorithm for factoring large integers can achieve an exponential speedup over the current best classical approaches. To realize this goal, however, researchers must design fault-tolerant protocols that deal with the fragile nature of quantum phenomena. In this broader context, this project will design efficient protocols to extract reliable information from noisy quantum devices. Another part of this project will use information-theoretic tools to study the information-processing power of quantum networks. The results are expected to have broad applications in quantum information science. The PIs will also mentor graduate students and provide undergraduate research opportunities in quantum technologies.The ability to distinguish quantum states is an important part of quantum communications and quantum information science. Even in relatively simple quantum systems, it can be difficult to design and implement good protocols for quantum state discrimination. One goal of this project is to answer the question: Are there efficient methods of quantum state discrimination that apply to large classes of practically relevant states? This is related to another part of the project, whose goal is to understand the strengths and limitations of quantum technology in the emerging era of noisy intermediate-scale quantum devices. This project will investigate the rate at which information and entanglement decay in noisy quantum networks. For instance, we will derive noise thresholds, below which information and entanglement can propagate through networks. Such results can be applied to fault-tolerant quantum computing and also to analyze information scrambling in chaotic quantum systems, such as black holes. Many research directions in this project are built upon mathematical tools for analyzing quantum systems, such as the strong data-processing inequality. The final part of this project will develop these tools and derive information-theoretic limits for quantum state discrimination and quantum networks.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.