Experimental realizations of routing or shuttling trapped ions in two dimensions in a quantum computer are extensively studied and discussed in various research articles, with particularly detailed examples in references [1, 2, 3, 6, 7, 9, 11, 13, 27, 42].

The selected references provide comprehensive empirical data and theoretical frameworks on the strategies and technologies employed for 2D ion movement in quantum computing environments. For instance, [2] demonstrates precise routing using a microfabricated X-junction surface trap, while [3] explores the use of a T-junction ion trap array for 2D ion handling. Additionally, reference [27] offers a deep theoretical insight into shuttling ions through corners and junctions in 2D arrays, connecting theoretical models directly to practical experiments, thereby enhancing the understanding of not only the implementation but also the optimization required for scalable quantum computing architectures.

Given the specific interest in the experimental realization of routing or shuttling trapped ions in 2D in quantum computers, the most important categories to highlight are those that provide clear data or detailed empirical studies on the mechanisms, technologies, and physical demonstrations of 2D ion shuttling, as well as theoretical and technological advancements that support these practical considerations. These categories provide a structure for understanding both the current state of technological application and the foundational technology that may influence future experimental achievements.

Category 1: Precisely Relevant Papers on 2D Ion Shuttling and Routing Description: Contains papers specifically discussing the experimental realization and data on manipulating quantum ion movement in a 2D structure within quantum computing systems. References: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 25, 27, 36, 42, 43, 44, 52, 69]

Category 2: Technological and Experimental Advances in 2D Ion Trap Configurations Description: These references detail the design, fabrication, and testing of 2D ion trap arrays, focusing on architectural and engineering advancements that enable effective 2D routing and shuttling. References: [14, 15, 16, 17, 18, 20, 21, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 45, 48, 51, 54, 55, 56, 59, 68, 73, 74, 76, 78]

Category 3: Theoretical Insights and Simulation Studies Relevant to 2D Ion Movement Description: Compiles studies that address theoretical issues, modeling, and simulation specific to two-dimensional ion dynamics, transport scenarios, and potential operations, supporting practical implementations. References: [27, 28, 42, 47, 49, 58, 63, 67, 69, 72, 73]

Category 4: Broader Advances in Quantum Computing and Ion Trap Technologies Description: Includes papers on broader aspects of quantum computing and ion trapping technologies that mention or imply 2D ion trapping or shuttling but mainly focus on general advancements in the field. References: [19, 46, 50, 53, 57, 60, 61, 62, 64, 65, 66, 70, 71, 75]