Exact Multimode Quantization of Superconducting Circuits via Boundary Admittance
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Quantum Physics arXiv:2601.04407 (quant-ph) [Submitted on 7 Jan 2026] Title:Exact Multimode Quantization of Superconducting Circuits via Boundary Admittance Authors:Mustafa Bakr, Robin Wopalenski View a PDF of the paper titled Exact Multimode Quantization of Superconducting Circuits via Boundary Admittance, by Mustafa Bakr and Robin Wopalenski View PDF HTML (experimental) Abstract:We show that the Schur complement of the nodal admittance matrix, which reduces a multiport electromagnetic environment to the driving-point admittance $Y_{\mathrm{in}}(s)$ at the Josephson junction, naturally leads to an eigenvalue-dependent boundary condition determining the dressed mode spectrum. This identification provides a four-step quantization procedure: (i) compute or measure $Y_{\mathrm{in}}(s)$, (ii) solve the boundary condition $sY_{\mathrm{in}}(s) + 1/L_J = 0$ for dressed frequencies, (iii) synthesize an equivalent passive network, (iv) quantize with the full cosine nonlinearity retained. Within passive lumped-element circuit theory, we prove that junction participation decays as, we prove that junction participation decays as $O(\omega_n^{-1})$ at high frequencies when the junction port has finite shunt capacitance, ensuring ultraviolet convergence of perturbative sums without imposed cutoffs. The standard circuit QED parameters, coupling strength $g$, anharmonicity $\alpha$, and dispersive shift $\chi$, emerge as controlled limits with explicit validity conditions. Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph) Cite as: arXiv:2601.04407 [quant-ph] (or arXiv:2601.04407v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.04407 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mustafa Bakr [view email] [v1] Wed, 7 Jan 2026 21:27:44 UTC (74 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact Multimode Quantization of Superconducting Circuits via Boundary Admittance, by Mustafa Bakr and Robin WopalenskiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.mes-hall math math-ph math.MP 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)