Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.06418 · Linear Algebra and its Applications

Perfect state transfer in Grover walks between states associated to vertices of a graph

Sho Kubota, Etsuo Segawa

Published Apr 19, 2022• 11 citations
arXivHTMLPDF
DOI
10.1016/j.laa.2022.04.006

Related papers

Periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs

Koushik Bhakta, Bikash Bhattacharjya

arXiv:2408.08715•Quantum Information Processing•Aug 11, 2025•1 citation

Circulant graphs with valency up to 4 that admit perfect state transfer in Grover walks

Sho Kubota, Kiyoto Yoshino

arXiv:2402.17341•Journal of Combinatorial Theory Series A•Apr 29, 2025•2 citations

Quantum walk on graphs and perfect state transfer

Rachel Elizabeth Bachman, Christino Tamon

•Aug 4, 2011•0 citations

State transfer in Grover walks on unitary and quadratic unitary Cayley graphs over finite commutative rings

Koushik Bhakta, Bikash Bhattacharjya

arXiv:2502.10217•Discrete Mathematics•Mar 31, 2026•0 citations

Grover walks on unitary Cayley graphs and integral regular graphs

Koushik Bhakta, Bikash Bhattacharjya

The unitary Cayley graph has vertex set $\{0,1, \hdots ,n-1\}$, where two vertices $u$ and $v$ are adjacent if $\gcd(u - v, n) = 1$. In this paper, we study periodicity and perfect state transfer of Grover walks on the unitary Cayley graphs. We characterize all periodic unitary Cayley graphs. We prove that periodicity is a necessary condition for occurrence of perfect state transfer on a vertex-transitive graph. Also, we provide a necessary and sufficient condition for the occurrence of perfect state transfer on circulant graphs. Using these, we prove that only four graphs in the class of unitary Cayley graphs exhibit perfect state transfer. Also, we provide a spectral characterization of the periodicity of Grover walks on integral regular graphs.

arXiv:2405.01020•May 2, 2024•0 citations

Perfect state transfer in Grover walks on association schemes and distance-regular graphs

Koushik Bhakta, Bikash Bhattacharjya

This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distance-regular graphs. We provide complete characterizations for exhibiting perfect state transfer on distance-regular graphs of diameter $2$ and diameter $3$, as well as integral distance-regular graphs.

arXiv:2506.07439•Jun 9, 2025•0 citations
The unitary Cayley graph has vertex set $\{0,1, \hdots ,n-1\}$, where two vertices uuu and vvv are adjacent if gcd⁡(u−v,n)=1\gcd(u - v, n) = 1gcd(u−v,n)=1. In this paper, we study periodicity and perfect state transfer of Grover walks on the unitary Cayley graphs. We characterize all periodic unitary Cayley graphs. We prove that periodicity is a necessary condition for occurrence of perfect state transfer on a vertex-transitive graph. Also, we provide a necessary and sufficient condition for the occurrence of perfect state transfer on circulant graphs. Using these, we prove that only four graphs in the class of unitary Cayley graphs exhibit perfect state transfer. Also, we provide a spectral characterization of the periodicity of Grover walks on integral regular graphs.
This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distance-regular graphs. We provide complete characterizations for exhibiting perfect state transfer on distance-regular graphs of diameter 222 and diameter 333, as well as integral distance-regular graphs.