A Scalable Superconducting Circuit Framework for Emulating Physics in Hyperbolic Space

Quantum Physics arXiv:2510.23827 (quant-ph) [Submitted on 27 Oct 2025] Title:A Scalable Superconducting Circuit Framework for Emulating Physics in Hyperbolic Space Authors:Xicheng Xu, Ahmed Adel Mahmoud, Noah Gorgichuk, Ronny Thomale, Steven Rayan, Matteo Mariantoni View a PDF of the paper titled A Scalable Superconducting Circuit Framework for Emulating Physics in Hyperbolic Space, by Xicheng Xu and 5 other authors View PDF HTML (experimental) Abstract:Theoretical studies and experiments in the last six years have revealed the potential for novel behaviours and functionalities in device physics through the synthetic engineering of negatively-curved spaces. For instance, recent developments in hyperbolic band theory have unveiled the emergence of higher-dimensional eigenstates -- features fundamentally absent in conventional Euclidean systems. At the same time, superconducting quantum circuits have emerged as a leading platform for quantum analogue emulations and digital simulations in scalable architectures. Here, we introduce a scalable superconducting circuit framework for the analogue quantum emulation of tight-binding models on hyperbolic and kagome-like lattices. Using this approach, we experimentally realize three distinct lattices, including, for the first time to our knowledge, a hyperbolic lattice whose unit cell resides on a genus-3 Riemann surface. Our method encodes the hyperbolic metric directly into capacitive couplings between high-quality superconducting resonators, enabling tenable reproduction of spectral and localization properties while overcoming major scalability and spectral resolution limitations of previous designs. These results set the stage for large-scale experimental studies of hyperbolic materials in condensed matter physics and lay the groundwork for realizing hyperbolic quantum processors, with potential implications for both fundamental physics and quantum computing Comments: Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph) Cite as: arXiv:2510.23827 [quant-ph] (or arXiv:2510.23827v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.23827 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Steven Rayan [view email] [v1] Mon, 27 Oct 2025 20:12:36 UTC (41,881 KB) Full-text links: Access Paper: View a PDF of the paper titled A Scalable Superconducting Circuit Framework for Emulating Physics in Hyperbolic Space, by Xicheng Xu and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cond-mat cond-mat.mes-hall cond-mat.other 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?)