Generalized exceptional quantum walk search

• URL: http://arxiv.org/abs/2011.01629v2
• Date: Wed, 4 Nov 2020 02:06:28 GMT
• Title: Generalized exceptional quantum walk search
• Authors: Meng Li and Yun Shang
• Abstract summary: We 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. We give two modified quantum walk models that can improve the success probability in the exceptional configurations.
• Score: 2.471925498075058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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