Generalized m-body mean-field projections for classical simulation of d-dimensional Heisenberg-picture dynamics
Abstract
Classical simulation of quantum many-body dynamics is challenged by the rapid growth of operator complexity, particularly in higher dimensions where tensor-network methods become increasingly demanding. We develop state-adapted Pauli-weight propagation based on generalized m-body mean-field projections, which compress many-body observables into optimal low-body representations in a covariance geometry induced by the initial state. Combined with adaptive Krylov-like restricted Heisenberg dynamics, this provides an alternative to conventional Hilbert--Schmidt Pauli-weight truncation. We derive necessary and conditional sufficient bounds on low-body approximation accuracy using standard operator complexity measures and characterize possible dynamical failure mechanisms of the state-adapted method. Numerical benchmarks demonstrate substantial state-dependent accuracy gains, while identifying regimes of reduced accuracy or violations of Pauli spectral bounds. For a three-dimensional system of $80$ interacting spins, our method achieves strong body-order convergence, close agreement with independently converging tensor-network simulations, and substantially smaller sparse Pauli representations. These results establish state-adapted Pauli propagation as a promising approach to classical simulation of higher-dimensional coherent many-body dynamics.
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BibTeX
@misc{perez2026generalized,
title = {{Generalized $m$-body mean-field projections for classical simulation of $d$-dimensional Heisenberg-picture dynamics}},
author = {Federico Tomás B. Pérez and Gabriela Wójtowicz and Matthias Kost and Martin B. Plenio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22069},
eprint = {2610.22069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22069},
}
RIS
TY - UNPB
TI - Generalized m-body mean-field projections for classical simulation of d-dimensional Heisenberg-picture dynamics
AU - Federico Tomás B. Pérez
AU - Gabriela Wójtowicz
AU - Matthias Kost
AU - Martin B. Plenio
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22069
UR - https://arxiv.org/abs/2610.22069
AB - Classical simulation of quantum many-body dynamics is challenged by the rapid growth of operator complexity, particularly in higher dimensions where tensor-network methods become increasingly demanding. We develop state-adapted Pauli-weight propagation based on generalized m-body mean-field projections, which compress many-body observables into optimal low-body representations in a covariance geometry induced by the initial state. Combined with adaptive Krylov-like restricted Heisenberg dynamics, this provides an alternative to conventional Hilbert--Schmidt Pauli-weight truncation. We derive necessary and conditional sufficient bounds on low-body approximation accuracy using standard operator complexity measures and characterize possible dynamical failure mechanisms of the state-adapted method. Numerical benchmarks demonstrate substantial state-dependent accuracy gains, while identifying regimes of reduced accuracy or violations of Pauli spectral bounds. For a three-dimensional system of $80$ interacting spins, our method achieves strong body-order convergence, close agreement with independently converging tensor-network simulations, and substantially smaller sparse Pauli representations. These results establish state-adapted Pauli propagation as a promising approach to classical simulation of higher-dimensional coherent many-body dynamics.
ER -