This paper studies the search for a single arc in a graph using the Szegedy walk. Arc search can be interpreted as finding a quantum particle not only in its position but also with a specific internal state. The quantum walk employed in this study is essentially the model proposed by Segawa and Yoshie for the purpose of edge search. First, we investigate how the symmetry of a graph is reflected in its time evolution matrix, and provide a sufficient condition under which the success probability of the search is independent of the marked arc. In particular, we prove that if a graph is arc-transitive, the success probability is independent of the choice of the marked arc. Next, we analyze path and cycle graphs and show that the quantum search is ineffective for these graphs, whereas it performs well for complete bipartite graphs $K_{n,n}$ . These results provide a theoretical foundation for studying arc and edge searches on various graphs, while also suggesting new problems concerning the eigenvalue analysis of edge-signed graphs in spectral graph theory.This paper studies the search for a single arc in a graph using the Szegedy walk. Arc search can be interpreted as finding a quantum particle not only in its position but also with a specific internal state. The quantum walk employed in this study is essentially the model proposed by Segawa and Yoshie for the purpose of edge search. First, we investigate how the symmetry of a graph is reflected in its time evolution matrix, and provide a sufficient condition under which the success probability of the search is independent of the marked arc. In particular, we prove that if a graph is arc-transitive, the success probability is independent of the choice of the marked arc. Next, we analyze path and cycle graphs and show that the quantum search is ineffective for these graphs, whereas it performs well for complete bipartite graphs $K_{n,n}$. These results provide a theoretical foundation for studying arc and edge searches on various graphs, while also suggesting new problems concerning the eigenvalue analysis of edge-signed graphs in spectral graph theory.

quant-pharXiv:2604.19134Apr 22, 20260 citations

A Query-Efficient Quantum Algorithm for Maximum Matching on General Graphs

Shelby Kimmel, R. Teal Witter

arXiv:2010.02324Lecture notes in computer scienceJan 1, 20214 citations

A Continuous - Time Quantum Walk for Attributed Graphs Matching

Tewabe Chekole

Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation /connection in the study of Quantum walks is furthermore described. Different Researchers had contribution and put their benchmark idea Pertaining with this research concept. I furthermore try to investigate recent Application of Quantum walks, In specific the problem pertained with Graph matching i.e Matching nodes(vertices) of the Graphs. In this research paper,I consider how Continuous-time quantum walk (CTQW) can be directed to Graph-matching problems. The matching problem is abstracted using weighted(attributed) Graphs that connects vertices's of one Graph to other and Try to compute the distance b/n those Graphs Node's Beside that finding the matched nodes and the Cost related to Matching. eventually measuring the distance between two Graphs which might have different size then by using k-nearest neighbor (k-NN) method try to classifying those graph based on closest training examples in the feature space.Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation /connection in the study of Quantum walks is furthermore described. Different Researchers had contribution and put their benchmark idea Pertaining with this research concept. I furthermore try to investigate recent Application of Quantum walks, In specific the problem pertained with Graph matching i.e Matching nodes(vertices) of the Graphs. In this research paper,I consider how Continuous-time quantum walk (CTQW) can be directed to Graph-matching problems. The matching problem is abstracted using weighted(attributed) Graphs that connects vertices's of one Graph to other and Try to compute the distance b/n those Graphs Node's Beside that finding the matched nodes and the Cost related to Matching. eventually measuring the distance between two Graphs which might have different size then by using k-nearest neighbor (k-NN) method try to classifying those graph based on closest training examples in the feature space.

arXiv:1801.10339Jan 31, 20180 citations

Quantum Algorithms for Matching Problems

Sebastian Dörn

Theory of Computing SystemsMay 29, 200819 citations

K_{n,n}

. These results provide a theoretical foundation for studying arc and edge searches on various graphs, while also suggesting new problems concerning the eigenvalue analysis of edge-signed graphs in spectral graph theory.