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The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…

Discrete Mathematics · Computer Science 2011-04-12 Milan Bašić

Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by…

Combinatorics · Mathematics 2019-01-08 Hiranmoy Pal , Bikash Bhattacharjya

For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between…

Quantum Physics · Physics 2016-05-10 R. Alvir , S. Dever , B Lovitz , J. Myer , C. Tamon , Y. Xu , H. Zhan

A continuous-time quantum walk on a graph is a matrix-valued function $\exp(-\mathtt{i} At)$ over the reals, where $A$ is the adjacency matrix of the graph. Such a quantum walk has universal perfect state transfer if for all vertices $u,v$,…

Quantum Physics · Physics 2017-01-20 Erin Connelly , Nathaniel Grammel , Michael Kraut , Luis Serazo , Christino Tamon

Quantum walks on undirected graphs have been studied using symmetric matrices, such as the adjacency or Laplacian matrix, and many results about perfect state transfer are known. We extend some of those results to oriented graphs. We also…

Combinatorics · Mathematics 2020-06-26 Chris Godsil , Sabrina Lato

We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part…

Quantum Physics · Physics 2018-07-26 Martin Stefanak , Stanislav Skoupy

A continuous-time quantum walk on a graph $G$ is given by the unitary matrix $U(t) = \exp(-itA)$, where $A$ is the Hermitian adjacency matrix of $G$. We say $G$ has pretty good state transfer between vertices $a$ and $b$ if for any…

We investigate quantum state transfer in XY spin chains and propose a recursive procedure to construct the nonuniform couplings of these chains with arbitrary length to achieve perfect state transfer(PST). We show that this method is…

Quantum Physics · Physics 2015-05-20 Yaoxiong Wang , Feng Shuang , Herschel Rabitz

We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove include: (1) The join of a weighted two-vertex…

Quantum Physics · Physics 2010-01-09 R. J. Angeles-Canul , R. Norton , M. Opperman , C. Paribello , M. Russell , C. Tamon

A blow-up of $n$ copies of a graph $G$ is the graph $\overset{n}\uplus~G$ obtained by replacing every vertex of $G$ by an independent set of size $n$, where the copies of vertices in $G$ are adjacent in the blow-up if and only if the…

Quantum Physics · Physics 2024-01-17 Bikash Bhattacharjya , Hermie Monterde , Hiranmoy Pal

A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…

Combinatorics · Mathematics 2018-05-24 Gabriel Coutinho , Chris Godsil

We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant…

Combinatorics · Mathematics 2018-08-20 Hanmeng Zhan

We propose a quantum network consisting of optical waveguides in the linear regime for quantum state transfer. The circular topology of our network introduces novel functionalities that enable us to analytically identify the conditions…

Quantum Physics · Physics 2026-05-12 Sunita Meena , Sugar Singh Meena , Paulo A Brandão , Amit Rai

It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped…

Quantum Physics · Physics 2010-07-14 M. A. Jafarizadeh , R. Sufiani , M. Azimia , F. Eghbali Fama

We study the existence of quantum state transfer in $\mathcal{Q}$-graphs in this paper. The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and…

Combinatorics · Mathematics 2021-08-18 Xiao-Qin Zhang , Shu-Yu Cui , Gui-Xian Tian

Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H_{A}(t):=\exp{(-itA)},\;t\in\Rl$. We say that the graph $G$ admits perfect state transfer between the verteices $u$ and $v$ at…

Combinatorics · Mathematics 2019-01-08 Hiranmoy Pal , Bikash Bhattacharjya

We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. Specific results we prove include: (1) The signed join of a negative 2-clique with any positive…

Quantum Physics · Physics 2013-01-17 J. Brown , C. Godsil , D. Mallory , A. Raz , C. Tamon

We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…

Quantum Physics · Physics 2022-11-30 Pierre-Antoine Bernard , Christino Tamon , Luc Vinet , Weichen Xie

Given a graph with Hermitian adjacency matrix $H$, perfect state transfer occurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix $\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant for…

Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is…

Combinatorics · Mathematics 2017-10-09 Chris Godsil , Krystal Guo , Mark Kempton , Gabor Lippner