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Pauli Propagation Enables Fast Classical Simulation of Strongly Correlated Quantum Systems

Chinmay Shrikhande1, Arnab Bachhar1, José Aarón Rodríguez-Jiménez1, Edward F. Valeev2, and Nicholas J. Mayhall1,*

  • *Contact author: nmayhall@iu.edu
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PRX Quantum 7, 043022 – Published 2 November, 2026

DOI: https://doi.org/10.1103/kq3v-whcq

Abstract

Ground-state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like Density Matrix Renormalization Group (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 sub-1% relative errors for Heisenberg and Hubbard lattices of up to 128 qubits. For a 10×10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 2 min on a single CPU thread, compared to over 50 h on 64 threads for DMRG. Accurate results are also obtained for systems that are difficult for quantum Monte Carlo: on the maximally frustrated 8×8 J1–J2 lattice and the hole-doped 8×8 Hubbard model, the tightest thresholds extrapolate to within a few tenths of a percent of the best published variational estimates. We further test vDBF on the 84-qubit π-valence active space of hexabenzocoronene, where the most reliable extrapolated correlation energies agree with DMRG to within 1%. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

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Popular Summary

Many of the most important problems in physics and chemistry, including high-temperature superconductivity, magnetism, and the electronic structure of large molecules, involve electrons that interact strongly with one another. The equations describing these “strongly correlated” systems become exponentially harder to solve as the number of electrons grows. Quantum computers were expected to handle such problems naturally, but classical algorithms have kept pace surprisingly well. In 2023, IBM reported that its 127-qubit quantum processor had simulated a system thought to lie beyond the reach of any classical computer. Within weeks, several research groups responded with classical methods, built on an idea called Pauli propagation, that matched or exceeded the quantum result. These algorithms were designed for a single purpose: stress testing quantum advantage claims. We show that the same machinery can be redirected toward a much older problem: finding the lowest energy configuration of a strongly correlated system. Our algorithm, the variational double bracket flow, recovers ground-state energies for 100-particle lattices in about 1 min on a single processor core, where the standard classical method requires dozens of hours on dozens of cores. It also works for a large organic molecule encoded onto 84 qubits, a regime where conventional approaches struggle. The work shows that algorithms developed to probe the boundary between classical and quantum computation can become practical tools for long-standing problems in chemistry and physics, and it sharpens the bar that quantum hardware must clear to demonstrate genuine advantage.

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PRX Quantum 7, 043022– Published 2 November, 2026
  • Received 31 May 2026
  • Revised 22 September 2026
  • Accepted 30 September 2026
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