Quantum search algorithms provide a way to speed up combinatorial search, and have found several applications in modern quantum technology. In particular, spatial search on graphs, based on continuous-time quantum walks (CTQW), represents a promising platform for the implementation of quantum search in condensed matter systems. CTQW-based algorithms, however, work exactly on complete graphs, while they are known to perform poorly on realistic graphs with low connectivity. In this paper, we put forward an alternative search algorithm, based on structuring the oracle operator, which allows one to improve the localization properties of the walker by tuning only the on-site energies of the graph, i.e., without altering its topology. As such, the proposed algorithm is suitable for implementation in systems with low connectivity, e.g., rings of quantum dots or superconducting circuits. Oracle parameters are determined by Hamiltonian constraints, without the need for numerical optimization.

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相当好的结构化Oracle改进简单图上的量子搜索

量子搜索算法提供了一种加速组合搜索的方法，并且在现代量子技术中发现了多种应用。特别地，基于连续时间量子游走（CTQW）的图形空间搜索代表了在凝聚态系统中实现量子搜索的有前途的平台。但是，基于CTQW的算法可完全在完整图形上运行，而众所周知，它们在具有低连通性的真实图形上的性能较差。在本文中，我们提出了一种基于构造预言算子的替代搜索算法，该算法允许仅通过调整图的现场能量（即不改变其拓扑）来改善步行者的定位特性。这样，所提出的算法适用于在低连通性的系统中实施，例如，量子点环或超导电路。Oracle参数由哈密顿约束确定，而无需进行数值优化。