Jay Gambetta
ACS Spring 2025
The constrained-search formulation of Levy and Lieb provides a concrete mapping from N-representable densities to the space of N-particle wave functions and explicitly defines the universal functional of density-functional theory. We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer, using a modified variational quantum eigensolver approach. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme featuring real-time computation of the Levy-Lieb functional along the search trajectory. We further illustrate a fidelity-based quantum kernel associated with the density to pure-state embedding implied by the Levy-Lieb procedure and employ the kernel for learning observable functionals of the density. We study the kernel's ability to generalize with high accuracy through numerical experiments on the Hubbard dimer.
Jay Gambetta
ACS Spring 2025
Thomas Alexander
QCE 2024
Zhancheng Yao, Martin Sandberg, et al.
MRS Fall Meeting 2024
Diana Chamaki, Stuart Hadfield, et al.
APS March Meeting 2023