Model Order Reduction for Parametric Dissipative Quantum Systems
Abstract
We consider reduced basis approximations of non-equilibrium steady states of parameter-dependent Lindbladians, whose ambient matrix space grows exponentially with system size. We give a unified structural view of the problem through its characterizations as an eigenvalue problem or as a trace-constrained source problem. Building on these characterizations, we propose a residual-driven reduced basis framework for both formulations. Under the assumption of a unique steady state, we derive residual-based state-error estimates, and establish (sub-)exponential convergence of the greedy algorithms under real-analytic parameter dependence of the problem data. Numerical experiments on boundary-driven Fermi--Hubbard and dissipative XYZ chains support the analysis and suggest that the trace-constrained greedy method offers the best overall balance of accuracy and computational cost.
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BibTeX
@misc{haasdonk2026model,
title = {{Model Order Reduction for Parametric Dissipative Quantum Systems}},
author = {Bernard Haasdonk and Benjamin Stamm and Zhuoyao Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12017},
eprint = {2610.12017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12017},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model Order Reduction for Parametric Dissipative Quantum Systems
AU - Bernard Haasdonk
AU - Benjamin Stamm
AU - Zhuoyao Zeng
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12017
UR - https://arxiv.org/abs/2610.12017
AB - We consider reduced basis approximations of non-equilibrium steady states of parameter-dependent Lindbladians, whose ambient matrix space grows exponentially with system size. We give a unified structural view of the problem through its characterizations as an eigenvalue problem or as a trace-constrained source problem. Building on these characterizations, we propose a residual-driven reduced basis framework for both formulations. Under the assumption of a unique steady state, we derive residual-based state-error estimates, and establish (sub-)exponential convergence of the greedy algorithms under real-analytic parameter dependence of the problem data. Numerical experiments on boundary-driven Fermi--Hubbard and dissipative XYZ chains support the analysis and suggest that the trace-constrained greedy method offers the best overall balance of accuracy and computational cost.
ER -