Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size

Roman Ovsiannikov; Kurt Jacobs; Andrii G. Sotnikov; Denys I. Bondar

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arXiv · 2609.25368

Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size

Roman Ovsiannikov·Kurt Jacobs·Andrii G. Sotnikov·Denys I. Bondar

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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 $D \approx 500$, and its runtime scales nearly linearly.

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Roman Ovsiannikov, Kurt Jacobs, Andrii G. Sotnikov, Denys I. Bondar. 2026-09-21. Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size. https://arxiv.org/abs/2609.25368

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