Symplectic H2 Model Reduction for High-Dimensional Linear Quantum Systems
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Quantum Physics arXiv:2605.07152 (quant-ph) [Submitted on 8 May 2026] Title:Symplectic H2 Model Reduction for High-Dimensional Linear Quantum Systems Authors:Alfo Borzi, Guofeng Zhang View a PDF of the paper titled Symplectic H2 Model Reduction for High-Dimensional Linear Quantum Systems, by Alfo Borzi and Guofeng Zhang View PDF HTML (experimental) Abstract:The $\mathcal{H}_2$ model reduction problem for high-dimensional linear quantum systems is studied under the constraint of physical realizability (PR). This constraint requires preservation of the canonical commutation relations and the quantum input-output structure, and therefore prevents the direct use of standard projection methods. A symplectic Petrov-Galerkin framework is presented, in which reduced-order models automatically satisfy the PR identities by construction. Within this framework, a symplectic variant of the iterative rational Krylov algorithm is developed and referred to as Quantum IRKA (Q-IRKA). At each iteration, an enriched tangential rational Krylov pool is generated from shifted linear solves. A symplectic basis is then extracted by a Gram-Schmidt-type procedure, paired with symplectic conjugates, and normalized so that the reduced trial space satisfies the canonical symplectic constraint. The interpolation points are updated from selected mirror images of the poles of the current reduced-order model, while the reduced-order matrices are obtained exclusively by structure-preserving projection. Numerical experiments on low-channel oscillator-chain systems and on a bosonic Kitaev-chain-inspired benchmark show that Q-IRKA is effective for large-scale linear quantum systems. Symplecticity and PR are preserved to machine precision, and accurate reduced-order models are obtained with moderate computational cost. The results also show that reduction quality depends substantially on dissipation geometry, channel placement, heterogeneity, and reduced order. These findings indicate that scalable $\mathcal{H}_2$ model reduction of linear quantum systems can be achieved while strictly preserving the underlying physical structure. Comments: Subjects: Quantum Physics (quant-ph); Systems and Control (eess.SY); Numerical Analysis (math.NA); Optimization and Control (math.OC) Cite as: arXiv:2605.07152 [quant-ph] (or arXiv:2605.07152v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.07152 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Guofeng Zhang [view email] [v1] Fri, 8 May 2026 02:38:57 UTC (1,779 KB) Full-text links: Access Paper: View a PDF of the paper titled Symplectic H2 Model Reduction for High-Dimensional Linear Quantum Systems, by Alfo Borzi and Guofeng ZhangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.NA cs.SY eess eess.SY math math.NA math.OC References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)