Quantum walk search for exceptional configurations on one- and two-dimensional lattice with extra long-range edges of HN4 network

• URL: http://arxiv.org/abs/2504.16664v1
• Date: Wed, 23 Apr 2025 12:33:42 GMT
• Title: Quantum walk search for exceptional configurations on one- and two-dimensional lattice with extra long-range edges of HN4 network
• Authors: Satoshi Watanabe, Pulak Ranjan Giri,
• Abstract summary: We study the emergence of several new exceptional configurations/vertices due to the additional long-range edges of the HN4 network on both one- and two-dimensional lattices.<n>It is also shown that a recently proposed modified coin can search all these configurations, including any other configurations in one- and two-dimensional lattices with very high success probability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There exist several types of configurations of marked vertices, referred to as the exceptional configurations, on one- and two-dimensional periodic lattices with additional long-range edges of the HN4 network, which are challenging to find using discrete-time quantum walk algorithms. In this article, we conduct a comparative analysis of the discrete-time quantum walk algorithm utilizing various coin operators to search for these exceptional configurations. First, we study the emergence of several new exceptional configurations/vertices due to the additional long-range edges of the HN4 network on both one- and two-dimensional lattices. Second, our study shows that the diagonal configuration on a two-dimensional lattice, which is exceptional in the case without long-range edges, no longer remains an exceptional configuration. Third, it is also shown that a recently proposed modified coin can search all these configurations, including any other configurations in one- and two-dimensional lattices with very high success probability. Additionally, we construct stationary states for the exceptional configurations caused by the additional long-range edges, which explains why the standard and lackadaisical quantum walks with the Grover coin cannot search these configurations.

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