Feedback-based quantum algorithm for ground state preparation of the Fermi-Hubbard model

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states have broad impacts. Variational quantum algorithms are one class of ground state algorithm that has received significant development in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving classical optimization problems that can become prohibitively expensive in high dimensions. We address this challenge through the development of a feedback-based quantum algorithm for ground state preparation that is inspired by quantum Lyapunov control and is optimization-free. We apply this approach to the Fermi-Hubbard model and present a variety of numerical illustrations that analyze different aspects of the algorithm and its performance.
Comment: 22 pages, 9 figures