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.

Companion paper to arXiv:2609.12840; 35 pages; 6 figures; supplementary numerical results and analytical proofs included. Comments and suggestions are appreciated

arXiv:2610.22069 [quant-ph]

(or arXiv:2610.22069v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.22069 arXiv-issued DOI via DataCite (pending registration)