CAREER: Quantum Information Theory of Many-body Physics

在自然界中，强相互作用的量子力学粒子系统可以形成一种新的物质相，其中系统的组成部分彼此强烈纠缠。虽然这样的阶段可以有潜在的变革性应用，如建立一个拓扑保护的容错量子计算机，这种纠缠的存在对我们的理解，表征和实验识别这些阶段提出了重大挑战。 PI将通过利用PI开创的称为纠缠引导程序的新理论框架来解决这些问题。这一理论框架将导致有效的方法来识别和表征强纠缠阶段的物质在实验中，并在经典计算机上的多体模拟的发展。PI还将制定一项全面的教育和推广计划，其中包括一名研究生和一名博士后学者的教育和培训。此外，研究活动将以一种广泛的研究人员都能接触到的形式传播。最后，PI将在加州戴维斯附近举办一个面向背景不足的大学生的量子计算和量子纠缠训练营，扩大不同背景的学生对量子信息科学领域的参与。该提案的主要科学目标是开发一个理论框架，可以从本地数据中预测长波长下强纠缠量子多体系统的特性，这些数据编码在本地约化密度矩阵中。利用纠缠引导程序的最新发展，PI将在以下问题上取得进展。首先，PI将发现可以表征多体量子相位的拓扑不变量。其次，PI将开发一种方法，从数值研究和实验中容易获得的数据中提取这些拓扑不变量。最后，通过研究量子边际问题的解决方案，PI将开发数值方法来模拟和解释相互作用的量子多体系统的低能特性。 该项目由NSF物理部和NSF材料研究部共同支持。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。

In nature, systems of strongly interacting quantum mechanical particles can form a novel phase of matter in which the constituents of the system are strongly entangled with each other. While such phases can have potentially transformative applications, such as building a topologically protected fault-tolerant quantum computer, the presence of such entanglement has posed a significant challenge in our understanding, characterization, and experimental identification of such phases. The PI will address these issues by leveraging a novel theoretical framework known as the entanglement bootstrap program, which was pioneered by the PI. This theoretical framework will lead to the development of efficient methods to identify and characterize strongly entangled phases of matter in experiments and in many-body simulations on classical computers. The PI will also develop a comprehensive education and outreach plan, which includes an education and training of a graduate student and a postdoctoral scholar. Moreover, the research activities will be disseminated in a form that is accessible to a broad set of researchers. Finally, the PI will host a bootcamp on quantum computing and quantum entanglement geared towards college students of underrepresented backgrounds near Davis, California, broadening the participation of students of diverse backgrounds to the field of quantum information science. The main scientific goal of this proposal is to develop a theoretical framework that can predict properties of strongly entangled quantum many-body systems at long wavelength from their local data, encoded in local reduced density matrices. Leveraging the recent development in the entanglement bootstrap program, the PI will make progress on the following problems. First, the PI will discover the topological invariants that can characterize many-body quantum phases. Second, the PI will develop a method to extract these topological invariants from the data that are readily available from numerical studies and experiments. Finally, by studying solutions to the quantum marginal problem, the PI will develop numerical methods to simulate and interpret low-energy properties of interacting quantum many-body systems. This project is jointly supported by the NSF Division of Physics and the NSF Division of Materials Research.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.