Certified Quantum Schr\"odinger Control via Hierarchical Tucker Models

Quantum Physics [Submitted on 20 Mar 2026] Certified Quantum Schrödinger Control via Hierarchical Tucker Models Nahid Binandeh Dehaghani, Rafal Wisniewski, A. Pedro Aguiar High-dimensional Schrödinger systems arising from tensor-product discretizations suffer from exponential state growth, making direct controller synthesis and real-time closed-loop simulation computationally challenging. Hierarchical Tucker (HT) tensor representations offer scalable low-rank surrogates, but the impact of fixed-rank truncation on closed-loop stability is not well understood. This paper develops a local robustness framework for sampled-data feedback control implemented with fixed-rank HT projections. By viewing each truncation as a bounded, rank-dependent perturbation of the nominal closed loop, and assuming a local phase-invariant contraction certificate together with trajectory-level hierarchical spectral decay, we show that the HT-projected dynamics are practically exponentially stable: trajectories converge to a dimension-independent tube whose radius decreases with the prescribed rank. We further obtain an explicit logarithmic rank-accuracy relation and establish conditions under which controllers designed on the HT-truncated surrogate model retain practical exponential tracking guarantees when deployed on the full system, together with an explicit bound quantifying the resulting surrogate-to-plant mismatch. A compact lattice example demonstrates the applicability of the framework. Comments: 6 pages, 1 figure Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20168 [quant-ph]   (or arXiv:2603.20168v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20168 Focus to learn more Submission history From: Nahid Binandeh Dehaghani [view email] [v1] Fri, 20 Mar 2026 17:46:50 UTC (572 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)