EAGER‐QAC‐QSA: Quantum Chemistry with Mean-field Cost from Semidefinite Programming on Quantum Computing Devices

芝加哥大学的David A. Mazziotti获得了化学系化学理论、模型和计算方法项目以及材料研究部凝聚态物质和材料理论项目的奖励，以利用量子计算的潜力来研究化学和材料科学中的问题。该提案是为了响应量子算法挑战Dear Colleague Letter， NSF 20-056而提交的。许多对改善社会至关重要的新分子和新材料是如此复杂，以至于很难在传统计算机上进行研究。Mazziotti和他的研究小组正在研究新的量子化学算法，利用量子计算机的优势，以更低的计算成本预测分子和材料的能量和其他特性。这项工作具有变革性的潜力，因为它旨在使应用能够应用于具有更多电子数量的更大分子，为化学和材料领域的量子计算开辟了新的前景。Mazziotti和他的团队也在推动教育和推广活动，包括芝加哥大学的化学量子计算课程，以及为芝加哥大学以外的本科生和高中生教授量子化学、信息和计算的交互式Zoom课堂系列。尽管在硬件和算法方面已经取得了显著的进步，但量子计算机相对于传统计算机的量子优势尚未在分子模拟中得到证明。当前和近期设备上的噪声限制了分子的大小和可处理的电子数量，使其低于经典极限。Mazziotti和他的研究小组正在寻求一种量子计算的新范式，在这种范式中，双电子减少密度矩阵（2-RDM）直接在量子计算机上计算。这种方法与所有现有的准备波函数并随后对目标可观测物进行测量的算法有很大的不同。直接制备2-RDM，在适当条件的约束下，强制其表示至少一个n-电子密度矩阵，不会遇到波函数模拟的传统瓶颈，如深度电路或非平凡的高维经典优化。具体而言，我们提出了一种量子半定规划（SDP）算法，用于量子计算机上2-RDM的直接变分计算。半定程序的量子解有可能将处理强电子相关的计算成本降低到平均场计算的计算成本。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。

David A. Mazziotti of The University of Chicago is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry and the Condensed Matter and Materials Theory program in the Division of Materials Research to harness the potential of quantum computing to study problems in chemistry and materials science. The proposal was submitted in response to the Quantum Algorithm Challenge Dear Colleague Letter, NSF 20-056. Many new molecules and materials that are critically important to improving society are so complex that they are difficult to study on conventional computers. Mazziotti and his research group are pursuing novel quantum chemistry algorithms that exploit the advantages of quantum computers to predict the energies and other properties of molecules and materials at a much lower computational cost. The work has the potential to be transformative in that it aims to enable applications to much larger molecules with larger numbers of electrons, opening new vistas for quantum computing in chemistry and materials. Mazziotti and his group are also driving educational and outreach activities including a quantum computing curricula for chemistry at the University of Chicago as well as an interactive Zoom classroom series for teaching quantum chemistry, information, and computing to undergraduate and high school students beyond the University of Chicago.Even though remarkable strides have been made in hardware and algorithms, a quantum advantage of quantum computers over classical computers has not been demonstrated in molecular simulations. Noise on current and near-term devices has limited the sizes of the molecules and the numbers of electrons that are treatable to below the classical limit. Mazziotti and his research group are pursuing a new paradigm for quantum computing in which the two-electron reduced density matrix (2-RDM) is computed directly on the quantum computer. This approach represents a dramatic departure from all existing algorithms that prepare the wave function and subsequently perform measurements of target observables. Direct preparation of the 2-RDM, constrained by suitable conditions to enforce its representation of at least one N-electron density matrix, does not encounter the traditional bottlenecks of wave function simulations such as deep circuits or non-trivial high-dimensional classical optimization. Specifically, we propose a quantum semidefinite programming (SDP) algorithm for the direct variational computation of the 2-RDM on quantum computers. The quantum solution of semidefinite programs has the potential to reduce the computational cost of treating strong electron correlation to that of a mean-field calculation.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.