Ground state energy estimation with a Sparse Pauli Dynamics-enabled Variational Double Bracket Flow

Estimating the ground-state energy of strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here, we present a variational double bracket flow (vDBF) algorithm that leverages Sparse Pauli Dynamics, a technique originally developed for classical simulation of quantum circuits, to approximate ground-state energies efficiently. By combining greedy operator selection with coefficient truncation and energy-variance extrapolation, the method achieves relative errors of less than 1% compared to DMRG benchmarks for both the Heisenberg and Hubbard models in one and two dimensions. We also benchmark the method using a polycyclic aromatic compound, hexabenzocoronene (HBC), and achieve chemically accurate results.