EAGER: QAC-QSA: Hamiltonian Reconstruction for Ansatz Selection and Validation of the Variational Quantum Eigensolver

康奈尔大学的Peter McMahon和Eun-ah Kim得到了化学系化学理论、模型和计算方法项目的一个热切奖项的支持，该奖项旨在开发使用量子计算机解决量子模拟问题的新方法。材料研究部的凝聚态物质和材料项目也共同资助了这一奖项。麦克马洪教授和金教授正在合作开发计算方法，以检查量子计算机是否计算出了量子化学或物理模拟问题的正确答案。量子计算机面临的一个挑战是，它们能够进行经典计算机无法进行的计算，因此有必要开发新的方法来确定量子计算机产生的答案是否有效，因为人们不能简单地将答案与经典计算机产生的结果进行比较。麦克马洪和金以及他们各自的团队正在开发的方法都可以检查答案，如果答案不正确，就会给出如何改进量子计算机上运行的算法的信息。这项工作立即在美国的量子计算行业产生了更广泛的影响，在美国，使用量子计算机解决化学和物理模拟问题的工作正在进行中，但需要验证方法。这项工作中正在进行的方法的开发和测试将通过开放共享代码和结果转移到行业实践中。从事这项研究的研究生将发展可转移的技能，这将帮助他们在量子信息科学的职业生涯中获得就业机会。量子凝聚态研究中的一个长期挑战是寻找或近似受挫量子自旋系统的基态的方法的发展。麦克马洪和金正在采用先前开发的哈密顿重建方法，以便有可能从变分量子本征解算器(VQE)算法在量子计算机中产生的量子态的测量结果中推断出最有可能产生VQE态的哈密顿量。为了评估哪类状态(即，VQE ansaetze)适合于特定问题，必须能够验证该类中的低能态与试图寻找其基态的哈密顿量是一致的。正是出于这个目的，McMahon和Kim正在使用带有VQE的哈密顿重建方法。McMahon和Kim正在将该方法应用于一个求解量子自旋模型的示例用例，该模型到目前为止拒绝所有经典方法，并且定义在2D正方形格子上，使其适合在许多近期量子计算机上执行。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Peter McMahon and Eun-Ah Kim of Cornell University are supported by an EAGER award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop new methods for using quantum computers to solve quantum-simulation problems. The Condensed Matter and Materials program in the Division of Materials Research also cofunds this award. Professors McMahon and Kim are collaborating to develop computational methods to check that a quantum computer has computed the correct answer to a quantum chemistry or physics simulation problem. A challenge with quantum computers is that they are able to do computations that classical computers cannot, and so it is necessary to develop new methods to determine if the answer produced by a quantum computer is valid or not because one cannot simply check the answer against what a classical computer can produce. The methods being developed by McMahon and Kim, and their respective groups, both allow the answer to be checked, and, if the answer is incorrect, give information on how to improve the algorithm being run on the quantum computer. This work has immediate broader impacts in the quantum-computing industry in the United States, where there is substantial effort underway to use quantum computers to solve both chemistry and physics simulation problems, but for which verification methods are needed. The development and testing of methods being conducted in this work will be transferred to industry practice through the open sharing of code and results. Graduate students working on this research will develop transferable skills that will help them gain employment in quantum information sciences careers. A longstanding challenge in quantum-condensed-matter research is the development of methods to find or approximate the ground states of frustrated quantum spin systems. McMahon and Kim are adapting previously developed Hamiltonian-reconstruction methods so that it is possible to infer, from measurements of the quantum states produced in a quantum computer by the Variational Quantum Eigensolver (VQE) algorithm, the Hamiltonian that is most likely to have given rise to the VQE state. In order to assess what classes of states (i.e., VQE ansaetze) are appropriate for a particular problem, it is necessary to be able to verify that low-energy states in that class are consistent with the Hamiltonian one is trying to find the ground state of. It is for this purpose that McMahon and Kim are using the Hamiltonian-reconstruction method with VQE. McMahon and Kim are applying the method with an example use case of solving a quantum spin model that has so far resisted all classical methods, and that is defined on a 2D square lattice, making it amenable to execution on many near-term quantum computers.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.