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Related papers: Perfect State Transfer on Abelian Cayley Graphs

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We show that a perfect quantum state transmission can be realized through a spin chain possessing a commensurate structure of energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry…

Quantum Physics · Physics 2009-11-10 T. Shi , Ying Li , Z. Song , C. P. Sun

We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more…

Combinatorics · Mathematics 2021-05-11 Ada Chan , Hanmeng Zhan

In this paper, we analyze state transfer in quantum walks by using combinatorial methods. We generalize perfect state transfer in two-reflection discrete-time quantum walks to a notion that we call 'peak state transfer'; we define peak…

Combinatorics · Mathematics 2025-01-14 Krystal Guo , Vincent Schmeits

In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding…

Quantum Physics · Physics 2022-09-19 Yusuke Ide , Akihiro Narimatsu

We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive…

Statistical Mechanics · Physics 2020-09-02 Jean Decamp , Jiangbin Gong , Huanqian Loh , Christian Miniatura

Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…

Quantum Physics · Physics 2007-05-23 M. Hein , J. Eisert , H. J. Briegel

High-fidelity quantum state transfer is critical for quantum communication and scalable quantum computation. Current quantum state transfer algorithms on the complete bipartite graph, which are based on discrete-time quantum walk search…

Quantum Physics · Physics 2023-02-24 Dan Li , Jia-Ni Huang , Yu-Qian Zhou , Yu-Guang Yang

In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure…

Quantum Physics · Physics 2023-08-16 Arthur Vesperini , Roberto Franzosi

We investigate quantum state transfer on a class of bipartite graphs, namely the butterfly graphs, within the framework of discrete-time quantum walks. These graphs facilitate the construction of scalable quantum networks that enable…

Quantum Physics · Physics 2026-04-14 Monika Rani , Subhashish Banerjee , Nikhil Swami , Supriyo Dutta

A perfect code in a graph $\Gamma = (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $\Gamma$ is a subset $C$…

Combinatorics · Mathematics 2026-05-19 Peter J. Cameron , Roro Sihui Yap , Sanming Zhou

Ballistic quantum-information transfer through spin chains is based on the idea of making the spin dynamics ruled by collective excitations with linear dispersion relation. Unlike perfect state transfer schemes, a ballistic transmission…

Quantum Physics · Physics 2015-12-03 Leonardo Banchi

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a…

The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…

Quantum Physics · Physics 2008-01-31 Constanza Riera , Stephane Jacob , Matthew G. Parker

Regular families of coupled quantum networks are described such the unknown state of a qubit can be perfectly routed from any node to any other node in a time linear in the distance. Unlike previous constructions, the transfer can be…

Quantum Physics · Physics 2011-01-17 Peter J. Pemberton-Ross , Alastair Kay

We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest neighbour interaction strengths…

Quantum Physics · Physics 2011-01-28 E. I. Jafarov , J. Van der Jeugt

Given two graphs $G_{1}$ of order $n_{1}$ and $G_{2}$, the neighborhood corona of $G_{1}$ and $G_{2}$, denoted by $G_{1}\bigstar G_{2}$, is the graph obtained by taking one copy of $G_{1}$ and taking $n_{1}$ copies of $G_{2}$, in the…

Combinatorics · Mathematics 2022-04-20 Xiao-Qin Zhang , Qi Xiong , Gui-Xian Tian , Shu-Yu Cui

Suppose $C$ is a subset of non-zero vectors from the vector space $\mathbb{Z}_2^d$. The cubelike graph $X(C)$ has $\mathbb{Z}_2^d$ as its vertex set, and two elements of $\mathbb{Z}_2^d$ are adjacent if their difference is in $C$. If $M$ is…

Combinatorics · Mathematics 2011-06-30 Wang-Chi Cheung , Chris Godsil

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…

Quantum Physics · Physics 2007-05-23 Nitin Saxena , Simone Severini , Igor Shparlinski

Quantum state transfer (QST) through spin chains has been extensively investigated. Two schemes, the coupling set for perfect state transfer (PST) or adding a leakage elimination operator (LEO) Hamiltonian have been proposed to boost the…

Quantum Physics · Physics 2023-09-26 Yang-Yang Xie , Feng-Hua Ren , Arapat Ablimit , Xiang-Han Liang , Zhao-Ming Wang

Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…

Quantum Physics · Physics 2026-05-05 Matheus R. de Jesus , Eduardo O. C. Hoefel , Renato M. Angelo