发表机构
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University; Shishan Laboratory, Suzhou Campus of Nanjing University; Hefei National Laboratory; Beijing Key Laboratory of Fault-Tolerant Quantum Computing, Beijing Academy of Quantum Information Sciences（南京大学固体微结构物理学院; 南京大学苏州校区石泉实验室; 合肥国家实验室; 北京量子信息科学研究院容错量子计算北京市重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用超导电路的参数空间构建双曲驱动量子系统（HDQS），实现双曲几何的量子模拟，阐明参数空间几何对可观测物理量的决定作用，建立了探索双曲流形量子动力学的通用平台。
AI 中文摘要
双曲几何承载着大量奇异量子现象，从全息对偶到新颖拓扑相均属此类。然而，受天然晶体材料的欧几里得约束影响，实验探究这些效应仍具挑战性。尽管近期合成晶格已实现静态实现，但它们往往缺乏探索完整几何景观所需的动态可调性。在此，我们通过在超导量子电路的参数空间内实现双曲几何的量子模拟，克服了这些局限。我们将双曲特性映射到动态可控哈密顿量参数上，构建了双曲驱动量子系统（HDQS）。通过探测该系统在几何量子驱动下的响应，我们阐明了参数空间的固有几何如何决定可观测物理量。此外，我们扩展了理论框架以实现系综模拟，这种泛化使我们能够利用超导量子比特的快速相干控制来捕获基本几何特征，为探索双曲流形上的量子动力学建立了通用平台。
英文摘要
Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remains challenging due to the Euclidean constraints of natural crystalline materials. While recent synthetic lattices have achieved static realizations, they often lack the dynamical tunability required to explore the full geometric landscape. Here, we overcome these limitations by implementing a quantum simulation of hyperbolic geometry within the parameter space of a superconducting quantum circuit. We construct a Hyperbolically Driven Quantum System (HDQS) by mapping the hyperbolic properties onto the dynamically controllable Hamiltonian parameters. By probing the systems' response under geometric quantum driving, we elucidate how the intrinsic geometry of the parameter space dictates observable physical quantities. Furthermore, we extend the theoretical framework to realize ensemble simulation. This generalization enables us to harness the fast coherent control of superconducting qubits to capture essential geometric characteristics, establishing a versatile platform for exploring quantum dynamics on hyperbolic manifolds.
