Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size
Abstract
The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below 10−5, the method is up to two orders of magnitude faster than QuTiP already at D ≈ 500, and its runtime scales nearly linearly.
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BibTeX
@misc{ovsiannikov2026lowrank,
title = {{Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size}},
author = {Roman Ovsiannikov and Kurt Jacobs and Andrii G. Sotnikov and Denys I. Bondar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25368},
eprint = {2609.25368},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25368},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size
AU - Roman Ovsiannikov
AU - Kurt Jacobs
AU - Andrii G. Sotnikov
AU - Denys I. Bondar
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25368
UR - https://arxiv.org/abs/2609.25368
AB - The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below 10^−5, the method is up to two orders of magnitude faster than QuTiP already at D ≈ 500, and its runtime scales nearly linearly.
ER -