This paper addresses frequency crowding in SNAIL-based superconducting quantum modules. First, we present design constraints by describing a physical model for realizable gates within a module, and building a fidelity model using error budgeting derived from device characteristics. Second, we tackle the allocation problem by analyzing the impact of frequency crowding on gate fidelity as the radix of the module increases. We explore whether the heuristic gate fidelity can be optimized with a discrete set of qubit frequencies while adhering to defined separation thresholds. By leveraging a combination of analytical and numerical techniques, we demonstrate scalable frequency allocation strategies that minimize spectator-induced errors. Our results further indicate that removing edges leads to improved gate fidelities while maintaining sufficient connectivity, suggesting that edge density is not a limiting factor for NISQ-scale benchmarks. The findings have implications for designing robust, high-fidelity quantum systems with practical constraints on hardware and connectivity.
Optimizing the frequency positioning of tunable couplers in a circuit QED processor to mitigate spectator effects on quantum operations
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克与卡弗里纳米科学研究所）；Orange Quantum Systems（橙量子系统）；Quantware B.V.（Quantware有限公司）
Tunable Hybrid-Mode Coupler Enabling Strong Interactions between Transmons at Centimeter-Scale Distance
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University（南京大学固体微结构物理学院）；Shishan Laboratory, Nanjing University（南京大学苏州校区）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学量子信息科学与技术江苏省重点实验室）
Breaking the scalability barrier via a vertical tunable coupler in 3D integrated transmon system
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University（南京大学固体微结构物理学院）；Shishan Laboratory, Nanjing University（南京大学时山实验室）；Jiangsu Key Laboratory of Ouantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）；Tencent Quantum Laboratory, Tencent（腾讯量子实验室）
Long-range tunable coupler for modular fluxonium quantum processors
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications（南京邮电大学量子信息与信息技术研究所）；South China Normal University（华南师范大学）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials（广东省量子工程与量子材料重点实验室）；Guangdong-Hong Kong Joint Laboratory of Quantum Matter（粤港澳量子物质联合实验室）；Frontier Research Institute for Physics, South China Normal University（华南师范大学物理前沿研究院）
A Tunable, Modeless, and Hybridization-free Cross-Kerr Coupler for Miniaturized Superconducting Qubits
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology（加州理工学院卡尔弗纳米科学研究所和托马斯·J·沃森Sr.应用物理实验室）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）
Fast CZ gate in hybrid fluxonium-transmon systems with tunable couplers
Nanjing University of Posts and Telecommunications（南京邮电大学）；Nanjing University（南京大学）；Shanxi University（山西大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Extensible Fluxonium Architecture Using Tunable Couplers with Low Shunt Capacitance
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications（南京邮电大学量子信息与科技研究院）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）；Key Laboratory of Atomic and Subatomic Structure and Quantum Control (South China Normal University), Ministry of Education（教育部原子与亚原子结构及量子控制重点实验室（华南师范大学））；School of Physics, South China Normal University（华南师范大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials（广东省量子工程与量子材料重点实验室）；Frontier Research Institute for Physics, South China Normal University（华南师范大学前沿物理研究所）
High-fidelity iSWAP gate with Double Transmon Coupler
University of Massachusetts, Lowell（马萨诸塞大学洛厄尔分校）；RTX BBN Technologies（RTX BBN科技公司）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Air Force Research Laboratory（空军研究实验室）；Northwestern University（西北大学）
Sign- and magnitude-tunable coupler for superconducting flux qubits
我们通过实验证实了磁通基超导量子比特的耦合元件的功能性，其耦合强度$J$的符号和幅度可以被调整{ \it in situ}。为了测量有效的$J$，耦合的两个量子位系统的基态已经被映射为施加到每个量子位的局部磁场的函数。系统的状态是通过直接读出单个量子位来确定的，同时抑制隧穿。这些测量结果表明，$J$可以从反铁磁通过零到铁磁调谐。
