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

在过去的几十年里，在材料和分子中发现了许多非常规的量子现象。这些量子多体现象有望在功能材料、量子信息、药物发现和催化剂设计方面具有革命性的应用。然而，由于粒子相互作用的复杂性，即使在最先进的超级计算机的帮助下，对这些现象背后的物理学的全面理论理解也是不切实际的。缺乏深刻的理解反过来又阻碍了这些现象的设计和应用。这个EAGER奖项支持研究和教育开发算法来解决这些量子现象，重点是电子和固体中原子振动之间强烈相互作用的材料。受这种相互作用的最新理论进展的激励，该项目旨在开发一种混合算法，利用经典计算机和现有量子计算机的优势。此外，研究小组还将应用这种新算法来解决量子材料中的几个特定开放问题，包括超导性和非平衡态。该项目将为各种量子多体现象提供可扩展的新型混合算法，并为设计功能材料提供理论指导。这一项目将有助于广大学生和学者的教育和专业发展。作为一门与物理、计算机科学、化学和材料科学相关的学科，研究成果将被纳入跨学科课程。克莱姆森大学和哈佛大学之间的合作将使文化和地理多样性的教育经验交流成为可能。本科生将通过暑期实习或研讨会参与研究项目，特别是少数族裔的参与。对量子多体系统，特别是具有强电子-电子和电子-声子相互作用的系统的定量理解是许多科学和技术领域的关键。由于它们的希尔伯特空间大小随粒子数量呈指数增长，在经典计算机中无法获得相关系统的满意解，需要量子计算技术。混合量子经典算法的最新进展构成了一个有希望的新方向，但现有的框架限制了它们在量子磁体或纯费米子系统中的应用。因此，需求和困难激发了新的量子算法的发展。该EAGER奖支持基于变分量子特征解算器和变分非高斯方法的最新进展，开发适用于相关电子-声子系统的混合量子经典算法的研究和教育。本项目包括两个具体目标：(i)开发一种适合于电子-声子系统基态计算的高精度量子算法；（ii）扩展了动力学和激励谱的评估算法。除了算法开发之外，这两个目标还包括解决凝聚态物理中的前沿问题，如超导性和物质的非平衡态。这项研究将推动量子算法的发展，并使无限大希尔伯特空间系统的应用成为可能。它将提供一个独特的工具来模拟相关量子多体系统的平衡和非平衡性质。此外，基于新算法的模拟将为理解一些实验现象提供物理见解，包括高tc超导和光致涌现相。这些见解对于功能材料的工程和设计至关重要。这项合作研究将为克莱姆森大学和哈佛大学的本科生和研究生提供一种新颖的教育体验。通过将最新的研究纳入课程和研讨会，影响也将扩大到没有直接参与这个项目的学生。部分资助的博士后将接受科学技能和实践技能的职业培训。通过夏季研究和研讨会活动，该项目将改善不同学生，特别是代表性不足的少数民族的科学教育。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。

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.