We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively and the known diagonal configuration can be regarded as its special case. Meanwhile, we give two modified quantum walk models that can improve the success probability in the exceptional configurations by numerical simulation. Furthermore, we introduce the concept of generalized exceptional configuration and consider search by quantum walk on a cycle with Grover coin. We find that the most natural coin combination model (G,-), where G is a Grover diffusion transformation, is a generalized exceptional configuration when just searching one marked vertex on the cycle. In the end, we find generalized exceptional configuration has a different evolution of quantum coherence from exceptional configuration. These extend largely the range of exceptional configuration of quantum walk search in some sense.

中文翻译：

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广义异常量子游走搜索

我们主要研究创造量子步行搜索的特殊配置。对于AKR算法在二维网格上的搜索，我们发现了一些AKR算法无法有效发现的新异常配置类，已知对角线配置可以看作是它的特例。同时，我们给出了两个改进的量子行走模型，通过数值模拟可以提高特殊配置下的成功概率。此外，我们引入了广义异常配置的概念，并考虑了使用 Grover 硬币在循环上进行量子行走搜索。我们发现最自然的硬币组合模型 (G,-)，其中 G 是 Grover 扩散变换，是仅在循环上搜索一个标记顶点时的广义异常配置。到底，我们发现广义异常配置具有与异常配置不同的量子相干演化。从某种意义上说，这些在很大程度上扩展了量子行走搜索的特殊配置范围。