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arXiv:2609.12840

State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics

Federico Tomás B. Pérez, Gabriela Wójtowicz, Martin B. Plenio

quant-phmath-phSubmitted Sep 11, 2026• Announced Sep 14, 2026• 0 citations
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Abstract

The Heisenberg picture can make quantum many-body simulation efficient when evolved observables admit compact operator representation within low-dimensional structures. Conventional Pauli-string propagation and truncation techniques exploit this structure, but in coherent Hamiltonian dynamics their error control is often heuristic and their stability can be poor. We introduce a state-adapted Krylov framework based on geometric generalized mean-field projections of many-body observables onto low-body operator subspaces. The resulting dynamics approximate expectation values, do not extend spatial support beyond that prescribed by Lieb-Robinson bounds, and compress high-body correlations onto their state-relevant low-body representatives rather than simply discarding them. We derive necessary operator-entanglement obstructions to low-body representation and conditional sufficient bounds on representation and dynamical errors involving nonstabilizerness and controlled high-body tails. Numerical benchmarks show improved, stable finite-$m$ hierarchies and simulations on large three-dimensional lattices, establishing a scalable state-adapted alternative to conventional Heisenberg-picture weight-truncation of Pauli strings.

Comments
10 pages, 5 figures. Comments and suggestions are welcome

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Generalized mmm-body mean-field projections for classical simulation of ddd-dimensional Heisenberg-picture dynamics
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