Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics¹, such as data storage, memory and logic². However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system^3,4. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure⁵. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting ‘particles’ using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions⁶, electrons and holes in two-dimensional materials^7,8, and topological insulators⁹, as well as colloids in soft materials^10,11,12,13.

当不能同时最小化有序晶格结构中的局部相互作用能时，就会出现几何挫折感，从而导致大量的简并状态。大量的简并配置可能导致微电子^1的实际应用，例如数据存储，存储器和逻辑²。但是，很难实现很高的简并性，尤其是在二维系统^3,4中。在这里，我们展示了二维磁通量子系统中具有高简并性的原位可控几何挫折。我们在超导薄膜中创建此薄膜，该薄膜位于可重构的人造自旋冰结构⁵下方。人造自旋冰中的可调磁电荷与超导体中的磁通量量子强烈相互作用，从而能够在受挫和结晶的磁通量量子状态之间进行切换。不同状态对超导临界电流曲线有可测量的影响，可以通过施加外部磁场来精确选择自旋冰磁态来重新配置。我们通过实现可重新编程的通量量子二极管，证明了这些效应的适用性。使用人工自旋冰对相互作用的“粒子”的能量构图进行裁剪，为几何挫折的设计提供了新的范例，这可能为控制其他材料系统（如磁性天functional）中的新功能开辟了道路⁶，二维材料^7,8中的电子和空穴，拓扑绝缘体⁹以及软材料^{10、11、12、13中的}胶体。