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

TL;DR

This paper introduces a novel variational double bracket flow algorithm utilizing Sparse Pauli Dynamics to efficiently estimate ground state energies of strongly correlated quantum systems, achieving high accuracy and significant speedups over traditional methods.

Contribution

The paper presents a new vDBF algorithm that combines Sparse Pauli Dynamics with greedy operator selection, enabling fast and accurate ground state energy estimation for complex quantum models.

Findings

Achieves less than 1% error compared to DMRG benchmarks.

Obtains results for a 10x10 Heisenberg lattice in about 10 minutes on a single CPU.

Demonstrates significant speedup over DMRG for large 2D quantum systems.

Abstract

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 Sparse Pauli Dynamics, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient truncation and energy-variance extrapolation, the method achieves less than 1% error relative to DMRG benchmarks for both Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 10 minutes on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For an 8x8 Hubbard model (128 qubits), the speedup is even more pronounced. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.