The Norton Theorem for Quantum Circuits and Systems

Quantum Physics arXiv:2607.16385 (quant-ph) [Submitted on 17 Jul 2026] Title:The Norton Theorem for Quantum Circuits and Systems Authors:Anthony J. Cressman, Rahul Sarpeshkar View a PDF of the paper titled The Norton Theorem for Quantum Circuits and Systems, by Anthony J. Cressman and 1 other authors View PDF HTML (experimental) Abstract:It is well known that classical analog circuits and systems benefit from the powerful Thevenin and Norton theorems. These theorems enable rigorous and exact mathematical simplification and representation of the effect of the rest of a system on the part we want to focus on. We show that there are corresponding versions of a "Quantum Norton Theorem" that enable exact simplification and reduction for quantum circuits and systems, not just for one port, but also for multiport and even open quantum systems. We demonstrate the method on two level systems, chains, system environment partitions, Lindblad examples, and Grover search. The Grover examples show how the reduced network isolates the bright pole governing ideal search and exposes how diagonal disorder transfers spectral weight into dark poles that degrade performance. By partitioning finite dimensional Schrodinger dynamics into retained and eliminated sectors, we show that Gaussian elimination gives an exact reduced equation in which the eliminated subsystem appears as a dynamical self energy and a source term. In the circuit representation, these terms become the Norton admittance and Norton current source seen by the retained quantum port. The same Schur complement construction extends to multiport reductions, composite system environment partitions, density matrix dynamics, and Lindblad evolution in Liouville space. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.16385 [quant-ph] (or arXiv:2607.16385v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.16385 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Anthony Cressman Jr [view email] [v1] Fri, 17 Jul 2026 17:26:48 UTC (12,552 KB) Full-text links: Access Paper: View a PDF of the paper titled The Norton Theorem for Quantum Circuits and Systems, by Anthony J. Cressman and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)