A Scalable Superconducting Circuit Framework for Emulating Physics in Hyperbolic Space

• URL: http://arxiv.org/abs/2510.23827v1
• Date: Mon, 27 Oct 2025 20:12:36 GMT
• 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,
• Abstract summary: We introduce a scalable superconducting circuit framework for the analogue quantum emulation of tight-binding models on hyperbolic and kagome-like lattices.<n>Our method encodes the hyperbolic metric directly into capacitive couplings between high-quality superconducting resonators.<n>These results set the stage for large-scale experimental studies of hyperbolic materials in condensed matter physics.
• Score: 0.08796261172196741
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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

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