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Yusuke Yoshie

Publications and source records attributed to Yusuke Yoshie.

6 recordsLinked to original sources
arXiv2022

Odd-periodic Grover walk

The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the characterization of graphs exhibiting a periodic Grover walk. Graphs having a periodic Grover walk with periods of $2, 3, 4$, and $5$ have previously been characterized. It is expected that graphs exhibiting a periodic Grover walk with odd period correspond to cycles with odd length. We address that problem and are able to perfectly characterize the class of graphs exhibiting an odd-periodic Grover walk by using a combinatorial method.

quant-ph↗
arXiv2022

A quantum searching model finding one of the edges of a subgraph in a complete graph

Some of the quantum searching models have been given by perturbed quantum walks. Driving some perturbed quantum walks, we may quickly find one of the targets with high probability. In this paper, we construct a quantum searching model finding one of the edges of a given subgraph in a complete graph. How to construct our model is that we label the arcs by $+1$ or $-1$, and define a perturbed quantum walk by the sign function on the set of arcs. After that, we detect one of the edges labeled $-1$ by the induced sign function as fast as possible. This idea was firstly proposed by Segawa et al. in 2021. They only addressed the case where the subgraph forms a matching, and obtained by a combinatorial argument that the time of finding one of the edges of the subgraph is quadratically faster than a classical searching model. In this paper, we show that the model is valid for any subgraph, i.e., we obtain by spectral analysis a quadratic speed-up for finding one of the edges of the subgraph in a complete graph.

quant-ph↗
arXiv2021

A new type of spectral mapping theorem for quantum walks with a moving shift on graphs

The conventional spectral mapping theorem for quantum walks can only be applied for walks employing a shift operator whose square is the identity. This theorem gives most of the eigenvalues of the time evolution $U$ by lifting the eigenvalues of an induced self-adjoint matrix $T$ onto the unit circle on the complex plane. We acquire a new spectral mapping theorem for the Grover walk with a shift operator whose cube is the identity on finite graphs. Moreover, graphs we can consider for a quantum walk with such a shift operator is characterized by a triangulation. We call these graphs triangulable graphs in this paper. One of the differences between our spectral mapping theorem and the conventional one is that lifting the eigenvalues of $T-1/2$ onto the unit circle gives most of the eigenvalues of $U$.

quant-ph↗
arXiv2020

Quantum search of matching on signed graphs

We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be regarded as so called the edge coloring. Then as an application, under an arbitrary edge coloring which gives a matching on a complete graph, we consider a quantum search of a colored edge from the edge set of a complete graph. We show that this quantum walk finds a colored edge within the time complexity of $O(n^{\frac{2-α}{2}})$ with probability $1-o(1)$ while the corresponding random walk on the line graph finds them within the time complexity of $O(n^{2-α})$ if we set the number of the edges of the matching by $O(n^α)$ for $0 \le α\le 1$.

quant-ph↗
arXiv2018

Periodicity of Grover walks on distance-regular graphs

Characterizations graphs of some classes to induce periodic Grover walks have been studied for recent years. In particular, for the strongly regular graphs, it has been known that there are only three kinds of such graphs. Here, we focus on the periodicity of the Grover walks on distance-regular graphs. The distance-regular graph can be regarded as a kind of generalization of the strongly regular graphs and the typical graph with an equitable partition. In this paper, we find some classes of such distance-regular graphs and obtain some useful necessary conditions to induce periodic Grover walks on the general distance-regular graphs. Also, we apply this necessary condition to give another proof for the strong regular graphs.

math.CO↗