发表机构
Technical University of Munich; TUM School of Natural Sciences; Physics Department; Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften; Munich Center for Quantum Science and Technology (MCQST)（慕尼黑工业大学; TUM自然科学学院; 物理系; 瓦尔特·迈斯纳研究所，巴伐利亚科学院; 慕尼黑量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究基于一阶电路量化方法，提出电路量子电动力学中用于精确黑箱量化和无散度有效模型的导纳公式，扩展黑箱量化框架至多端口等场景，为超导量子硬件电磁设计提供新途径。
AI 中文摘要
基于一阶电路量化方法[arXiv:2304.12252, arXiv:2401.09120]，我们提供简单公式，用于构建基于约瑟夫森结的超导量子多态系统（qudit）与无源线性环境以电容、电感或电流方式耦合的精确哈密顿量。这些环境可以是多端口、多模、离散或连续、互易或非互易的，直接由其阻抗或导纳矩阵表征。在弱耦合区域，我们进一步推导了针对模分辨环境的无散度色散哈密顿量，以及针对耗散连续体的跃迁分辨弱耦合主方程。模结构、频率重整化、环境介导的相互作用、衰减率和定向交叉耦合均来自同一因果导纳响应，同时明确并避免了先前处理中因未受控近似产生的虚假兰姆移位散度。我们将该理论应用于一组示例电路，包括离散谐振器滤波器、有限带超材料环境、非互易波导量子电动力学系统和超导巨原子，这些电路可获得解析响应矩阵，尽管该方法特别适用于电磁求解器的数值响应或实验表征。我们由此将黑箱量化框架扩展至多端口、耗散和非互易场景，为大规模超导量子硬件的优化和自动化电磁设计建立了简单且可扩展的途径。
英文摘要
Building on the first-order circuit quantization method [arXiv:2304.12252, arXiv:2401.09120], we provide simple formulas to construct exact Hamiltonians for Josephson-junction-based superconducting qudits capacitively, inductively, or galvanically coupled to passive linear environments. These environments may be multiport, multimode, discrete or continuous, reciprocal or nonreciprocal, and are characterized directly by their impedance or admittance matrices. In the weak-coupling regime, we further derive \emph{divergence-free} dispersive Hamiltonians for mode-resolved environments and transition-resolved weak-coupling master equations for dissipative continua. Mode structure, frequency renormalizations, environment-mediated interactions, decay rates, and directional cross couplings then follow from the same causal immittance response, while spurious Lamb-shift divergences arising from uncontrolled approximations in previous treatments are made explicit and avoided. We apply the theory to a set of illustrative circuits comprising a discrete resonator filter, finite-band metamaterial environments, nonreciprocal waveguide-QED systems, and superconducting giant atoms, for which analytical response matrices can be obtained, although the method is particularly well suited to numerical responses from electromagnetic solvers or experimental characterization. We thereby extend the black-box quantization framework to multiport, dissipative, and nonreciprocal settings, establishing a simple and scalable route toward optimized and automated electromagnetic design of large-scale superconducting quantum hardware.
Comments48 pages. 20 Figures. New App. D for time-dependent flux allocation
