Characterizing Finite-Temperature Topology Via Quantum Computation

量子计算机的快速发展为我们带来了一个强大的工具，可以用来探索物理、化学、生物、金融和其他一些使用现有经典计算机几乎不可能解决的具有挑战性的问题。与此同时，具有奇异性质的新型量子物质的发现，可以通过拓扑学的概念来理解，这彻底改变了我们对电或热应用材料的分类。虽然温度往往会破坏量子计算和拓扑物质，但存在一些保护措施，有待系统的表征。这项研究将通过应用量子计算加速研究有限温度下拓扑量子物质的悬而未决的问题，并发现抗温度破坏的量子计算新方案的稳健量子性质，从而推动科学和技术的进步。从研究中得到的受拓扑性质保护的量子行为的表征将导致用于信息存储和处理的新的功能量子材料和更容易获得的量子计算机。这项研究将在加利福尼亚州中央山谷的当地社区传播和广播，那里的少数民族人口比例较低。虽然零温拓扑量子物质的元素周期表已经建立起来，但由于同时包含量子分布和热分布，系统地刻画有限温度下的拓扑物质仍然是一个挑战。通过提纯和几何构造的过程，有限温度系统可以获得一种形式，允许在量子计算机上利用其来自量子本质的力量来求解它们。这项研究将首先在量子计算机上证明简单系统的有限温度拓扑性质，然后系统地将更复杂的拓扑物推广到有限温度。利用这些健壮的拓扑特性，这项研究将反过来设计出对温度具有健壮性的新的量子计算方案，并使用量子计算来连接高能物理和量子信息界开发的有限温度量子理论。此外，这项研究将在本科生和研究生课程中引入实用量子计算，以培养量子教育和行业的下一代劳动力。这一奖项反映了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。

The rapid development of quantum computers has brought us a powerful tool for exploring challenging problems in physics, chemistry, biology, finance, and others that are practically impossible using available classical computers. Meanwhile, the discovery of novel quantum matter with exotic properties that can be understood via the concept of topology has revolutionized our classification of materials for electric or thermal applications. While temperature tends to destroy both quantum computation and topological matter, there exist protections which await systematic characterization. This research will advance both science and technology by applying quantum computation to accelerate the investigation of the open question on topological quantum matter at finite temperature and discoveries of robust quantum properties for novel schemes of quantum computation against destructions from temperature. The characterization of quantum behavior protected by topological properties from the research will lead to new functional quantum materials for information storage and processing and more accessible quantum computers. The research will be disseminated and broadcast to local communities in the California Central Valley with a high population of under-represented minorities. While a periodic table of topological quantum matter at zero temperature has been constructed, a systematic characterization of topological matter at finite temperature remains a challenge due to the inclusion of both quantum and thermal distributions. Through the process of purification and geometric construction, finite-temperature systems can acquire a formalism that allows them to be solved on quantum computers using its power from the quantum nature. This research will first demonstrate finite-temperature topological properties of simple systems on quantum computers and then systematically generalize more complicated topological matter to finite temperature. Utilizing those robust topological properties, the research will in turn design novel quantum computational schemes robust against temperature and use quantum computation to bridge finite-temperature quantum theories developed by high-energy physics and quantum-information communities. Moreover, the research will introduce practical quantum computation to undergraduate and graduate curricula to train the next generation of workforce in quantum education and industry.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.