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

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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.