Effective Study of Superconducting Quantum Circuits

Quantum Physics arXiv:2609.25296 (quant-ph) [Submitted on 21 Sep 2026] Title:Effective Study of Superconducting Quantum Circuits Authors:Carlos Raul Javier Valdez, Hector Hugo Hernandez Hernandez, Guillermo Chacon-Acosta View a PDF of the paper titled Effective Study of Superconducting Quantum Circuits, by Carlos Raul Javier Valdez and 2 other authors View PDF HTML (experimental) Abstract:We apply the momentous quantum mechanics formalism to the non-perturbative study of superconducting circuits in the transmon regime, deriving effective equations of motion for the bare Josephson junction (JJ), the cavity--JJ system, and a dissipative resonator. A Gaussian closure on the hierarchy of quantum moments resums the full cosine nonlinearity into the closed-form effective Hamiltonian $\tfrac{1}{2}[V(\phi+\phi_s)+V(\phi-\phi_s)]$, which is non-perturbative and preserves the periodicity and boundedness of the Josephson potential at all phase amplitudes; the standard Kerr (Duffing) approximation is recovered as a special case. We derive the quantum-dressed frequency $\omega_{\rm eff}=\Omega_p\sqrt{\cos(\phi_{\rm zpf}/\phi_0)}$, and benchmark the effective dynamics against exact Mathieu-function diagonalization, with the quantum width $G^{2,0}(t)$ providing the most sensitive diagnostic of the closure's validity and marks the boundary of the Gaussian approximation more sharply than $\langle\hat\phi\rangle(t)$ does. We compare the Caldirola--Kanai, Bateman, and Lindblad descriptions: the Bateman dynamics, quantized with a switched symplectic structure, preserves the Heisenberg bound, admits exact closed-form moment solutions, and reproduces the Lindblad benchmark for weak damping, i.e., within the analytic error bound $(\lambda/\omega_1)^2\,\phi_{\rm zpf}^2$. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.25296 [quant-ph] (or arXiv:2609.25296v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.25296 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Carlos Raul Javier Valdez [view email] [v1] Mon, 21 Sep 2026 18:40:54 UTC (14,968 KB) Full-text links: Access Paper: View a PDF of the paper titled Effective Study of Superconducting Quantum Circuits, by Carlos Raul Javier Valdez and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)