EAGER-QAC-QSA: Quantum Algorithms for Correlated Electron-Phonon System

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Non-Technical SummaryIn the past few decades, many unconventional quantum phenomena have been discovered in materials and molecules. These quantum many-body phenomena are expected to have revolutionary applications in functional materials, quantum information, drug discovery, and catalyst design. However, due to the complexity originating from interacting particles, a comprehensive theoretical understanding of the physics behind these phenomena is impractical even with the help of state-of-the-art supercomputers. That lack of profound understanding, in turn, hinders the design and application of these phenomena.This EAGER award supports research and education on developing algorithms to address these quantum phenomena, with a focus on materials with strong interactions between the electrons and the vibrations of the atoms in the solid. Motivated by recent theoretical progress on this type of interaction, this project aims to develop a hybrid algorithm that takes advantage of both classical computers and existing quantum computers. In addition, the research team will also apply this new algorithm to address several specific open questions in quantum materials, including superconductivity and nonequilibrium states. This project will provide both a new class of hybrid algorithms extensible for various quantum many-body phenomena and a theoretical guideline for designing functional materials.This project will contribute to the education and professional development of a broad pipeline of students and scholars. As a subject related to physics, computer science, chemistry, and materials science, the research outcomes will be incorporated into interdisciplinary courses. The collaboration between Clemson University and Harvard University will allow for the exchange of educational experiences with cultural and geographical diversity. Undergraduate students will be involved in the research project through summer internships or workshops, with the particular involvement of underrepresented minorities.Technical SummaryThe quantitative understanding of quantum many-body systems, especially systems with both strong electron-electron and electron-phonon interactions, is the key to many areas of science and technology. Due to the exponential growth of their Hilbert space sizes with the number of particles, a satisfactory solution for correlated systems is not accessible in classical computers and requires quantum computing techniques. Recent progress in hybrid quantum-classical algorithms constitutes a promising new direction, but the existing framework restricts their application to quantum magnets or pure fermionic systems. Therefore, the demands and difficulties motivate the development of new quantum algorithms.This EAGER award supports research and education on developing a hybrid quantum-classical algorithm applicable to correlated electron-phonon systems, based on recent progress in the variational quantum eigensolver and the variational non-Gaussian approach. This project includes two specific goals: (i) to develop a high-accuracy quantum algorithm suitable for the ground-state calculation of electron-phonon systems; (ii) to extend the algorithm for the evaluation of dynamics and excitation spectrum. In addition to algorithm development, both goals include applications for solving cutting-edge problems in condensed matter physics, such as superconductivity and nonequilibrium states of matter.This research will advance quantum algorithms and enable applications for systems with infinitely large Hilbert spaces. It will provide a unique tool to simulate the equilibrium and nonequilibrium properties of relevant quantum many-body systems. Moreover, the simulations based on the new algorithm will provide physical insights into understanding a few experimental phenomena, including high-Tc superconductivity and photoinduced emergent phases. These insights are crucial for the engineering and design of functional materials.This collaborative research will provide a novel educational experience for undergraduate and graduate students at Clemson University and Harvard University. By incorporating the latest research into courses and seminars, the impact will also extend to students who are not directly involved in this project. The postdoc partially supported by this grant will receive career training in both scientific and practical skills. Through summer research and workshop activities, this project will improve science education among diverse students, particularly underrepresented minorities.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.