Related papers: Universality in perfect state transfer
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…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
We study a continous-time quantum walk on a path graph. In this paper, we show that, for any odd prime $p$ and positive integer $t$, the path on $2^t p - 1$ vertices admits pretty good state transfer between vertices $a$ and $n+1-a$ for…
Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk is well investigated. However, the…
We define the quaternionic quantum walk on a finite graph and investigate its properties. This walk can be considered as a natural quaternionic extension of the Grover walk on a graph. We explain the way to obtain all the right eigenvalues…
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions…
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…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have equal weights. In this paper, we explore the role of twin…
A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…
In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk;…
Quantum state transfer between different sites is a significant problem for quantum networks and quantum computers. By selecting quantum walks with two coins as the basic model and two coin spaces as the communication carriers, we…
We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex the search algorithm finds the…
We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time.…
Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal…
We suggest a scheme that allows arbitrarily perfect state transfer even in the presence of random fluctuations in the couplings of a quantum chain. The scheme performs well for both spatially correlated and uncorrelated fluctuations if they…
We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…