EPSCOR Research Fellows: NSF: Quantum Advantage in Random Quantum Hamiltonians

This Research Infrastructure Improvement (RII) EPSCoR Research Fellows project will provide a fellowship to an Assistant professor and training for an undergraduate student at Bowdoin College. This work will be conducted in collaboration with Dr. David Gamarnik at the Massachusetts Institute of Technology. Random quantum Hamiltonians are canonical models for many-body physics and are among the strongest candidates for physics problems for which quantum computers may be more effective at solving than classical computers would be. These models capture complex phenomena, yet from an algorithmic perspective, the field still lacks a rigorous understanding of questions such as when do these models transition from “easy” to “hard” for classical and quantum computing algorithms. This fellowship project will use tools and theory at the interface of mathematics, physics, and computer science and study models that are important both for understanding quantum physics and testing the capabilities of future quantum computers. The fellowship will expand research in quantum information science in Maine, train undergraduate researchers at Bowdoin College to prepare them for a future in STEM, and connect students to an active research ecosystem in the Boston area. This project will advance the understanding of random quantum Hamiltonians, a class of models with randomly generated interactions studied in computer science, quantum information science and statistical physics. The work will focus on three areas: (1) identifying when analytic methods can provably approximate free energy and other thermal properties; (2) analyzing geometric structures like the overlap gap property to produce sharp algorithmic thresholds for sampling, optimization, and state preparation; and (3) implementing saddle point solvers for systems of partial differential equations arising from replica analyses of random quantum Hamiltonians. The project will combine tools from statistical physics, approximation theory, spin-glass theory, and numerical analysis. Code will be made open source for benchmarking and future reproducible study. The fellowship will strengthen Bowdoin’s research in quantum information science, advance the PI’s independent research program, train an undergraduate researcher, and deepen ties between Bowdoin College and the Massachusetts Institute of Technology. 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.