Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.25368

Authors: Ovsiannikov, Roman, Jacobs, Kurt, Sotnikov, Andrii G., Bondar, Denys I.

Institutions: Kharkiv Institute of Physics and Technology, DEVCOM Army Research Laboratory, United States Army Combat Capabilities Development Command, University of Massachusetts Boston, United States Army, V. N. Karazin Kharkiv National University, Tulane University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Army Research Office

OpenAlex ID: W7214122428

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