State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics
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.
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BibTeX
@misc{perez2026stateadapted,
title = {{State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics}},
author = {Federico Tomás B. Pérez and Gabriela Wójtowicz and Martin B. Plenio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12840},
eprint = {2609.12840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12840},
}
RIS
TY - UNPB
TI - State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics
AU - Federico Tomás B. Pérez
AU - Gabriela Wójtowicz
AU - Martin B. Plenio
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12840
UR - https://arxiv.org/abs/2609.12840
AB - 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.
ER -