Characterizing Finite-Temperature Topology Via Quantum Computation

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.