Characterizing Finite-Temperature Topology Via Quantum Computation

量子计算机的快速发展给我们带来了一个强大的工具，用于探索物理、化学、生物、金融和其他领域的挑战性问题，这些问题使用现有的经典计算机几乎是不可能的。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。虽然温度倾向于破坏量子计算和拓扑物质，但存在等待系统表征的保护措施。本研究将通过应用量子计算来加速研究有限温度下拓扑量子物质的开放问题，并发现抗温度破坏量子计算新方案的鲁棒量子特性，从而推动科学和技术的发展。该研究中受拓扑特性保护的量子行为特征将导致用于信息存储和处理的新型功能量子材料以及更容易使用的量子计算机。这项研究将向加利福尼亚中央山谷的当地社区散发和广播，那里有大量未被充分代表的少数民族。虽然已经建立了零温度下拓扑量子物质的周期表，但由于包含量子和热分布，有限温度下拓扑物质的系统表征仍然是一个挑战。通过净化和几何构造的过程，有限温度系统可以获得一种形式，使其能够在量子计算机上利用其量子性质的力量进行求解。本研究将首先在量子计算机上展示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质推广到有限温度。利用这些鲁棒拓扑特性，该研究将反过来设计新的抗温度量子计算方案，并使用量子计算来连接由高能物理和量子信息社区开发的有限温度量子理论。此外，该研究将在本科和研究生课程中引入实用的量子计算，以培养量子教育和工业的下一代劳动力。该奖项反映了美国国家科学基金会的法定使命，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。

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.