Pauli propagation enables fast classical simulation of strongly correlated quantum systems
Ground state energy estimation for 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 Pauli Propagation, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient-based fluctuation truncation and energy-variance extrapolation, we obtain results with sub-1% relative accuracy compared to DMRG benchmarks for the Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 1 minute on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For the 8x8 half-filled Hubbard model, corresponding to 128 qubits, vDBF reaches the 1% error regime in less than one hour, while our DMRG calculations required more than 10 hours on 64 threads. We further test vDBF on the 84-qubit π-valence active space of hexabenzocoronene, where the tighter-threshold calculations achieve sub-1% agreement with DMRG. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.