An infinite family of circulant graphs with perfect state transfer in discrete quantum walks

Zhan, Hanmeng

doi:10.1007/s11128-019-2483-3

Cited by 27 publications

(19 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The phenomenon of perfect state transfer (PST) in quantum communication networks was originally introduced by Bose in [14]. This work has attracted much research interest since many applications have been found in quantum information processing and cryptography (see [1,2,3,5,11,15,17,18,34,38,37] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case

Cao¹,

Chen

Ling³

2020

Electron. J. Combin.

View full text Add to dashboard Cite

Recently, perfect state transfer (PST for short) on graphs has attracted great attention due to their applications in quantum information processing and quantum computations. Many constructions and results have been established through various graphs. However, most of the graphs previously investigated are abelian Cayley graphs. Necessary and sufficient conditions for Cayley graphs over dihedral groups having perfect state transfer were studied recently. The key idea in that paper is the assumption of the normality of the connection set. In those cases, viewed as an element in a group algebra, the connection set is in the center of the group algebra, which makes the situations just like in the abelian case. In this paper, we study the non-normal case. In this case, the discussion becomes more complicated. Using the representations of the dihedral group $D_n$, we show that ${\rm Cay}(D_n,S)$ cannot have PST if $n$ is odd. For even integers $n$, it is proved that if ${\rm Cay}(D_n,S)$ has PST, then $S$ is normal.

show abstract

Section: Introductionmentioning

confidence: 99%

Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case

Cao¹,

Chen

Ling³

2020

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

“…These partitions may arise from other graph structures, such as orientable embeddings [25]. The spectral decomposition of a tworeflection walk has been studied [20], and used to find perfect state transfer in circulant graphs [24].…”

Section: Two-reflections Modelmentioning

confidence: 99%

Discrete-time quantum walks and graph structures

Godsil

Zhan

2019

Journal of Combinatorial Theory, Series A

Self Cite

View full text Add to dashboard Cite

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total entropies of the average mixing matrices for some cubic graphs. The trace captures how likely a quantum walk is to revisit the state it started with, and the total entropy measures how close the limiting distribution is to uniform. Our numerical results indicate three relations between quantum walks and graph structures: for the first model, rotation systems with higher genera give lower traces and higher entropies, and for the second model, the symmetric 1-factorizations always give the highest trace.

show abstract

“…We refer [3,21] for example. Although not as numerous as in continuous-time quantum walks, we can find studies of perfect state transfer also in discrete-time quantum walks [2,16,17,19,23,24,26,27,28]. These studies are briefly summarized in Section 1 of [27].…”

Section: Introductionmentioning

confidence: 99%

“…Although not as numerous as in continuous-time quantum walks, we can find studies of perfect state transfer also in discrete-time quantum walks [2,16,17,19,23,24,26,27,28]. These studies are briefly summarized in Section 1 of [27]. Recently, state transfer in discrete-time quantum walks has been studied also from the viewpoint of algebraic graph theory.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, state transfer in discrete-time quantum walks has been studied also from the viewpoint of algebraic graph theory. Zhan [27] has constructed an infinite family of 4-regular circulant graphs on which perfect state transfer occurs. Chan and Zhan [4] have established the theory for pretty good state transfer in discrete-time quantum walks.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Kubota¹,

Segawa²

2021

Preprint

View full text Add to dashboard Cite

We study perfect state transfer in Grover walks, which are typical discretetime quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer between vertex type states can be studied via Chebyshev polynomials. We derive a necessary condition on eigenvalues of a graph for perfect state transfer between vertex type states to occur. In addition, we perfectly determine the complete multipartite graphs whose partite sets are the same size on which perfect state transfer occurs between vertex type states, together with the time.

show abstract

An infinite family of circulant graphs with perfect state transfer in discrete quantum walks

Cited by 27 publications

References 36 publications

Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case

Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case

Discrete-time quantum walks and graph structures

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

Contact Info

Product

Resources

About