Related papers: Zero Transfer in Continuous Time Quantum Walks
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
Quantum walks exhibit properties without classical analogues. One of those is the phenomenon of asymptotic trapping -- there can be non-zero probability of the quantum walker being localised in a finite part of the underlying graph…
Quantum transport across discrete structures is a relevant topic of solid state physics and quantum information science, which can be suitably studied in the context of continuous-time quantum walks. The addition of phases degrees of…
In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We address routing of classical and quantum information over quantum network, and show how to exploit chirality to achieve nearly optimal and robust transport. In particular, we prove how continuous time chiral quantum walks over a minimal…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of…
Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim…
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,…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous time quantum walks on quantum networks based on certain circulant graphs with $2^k$ $\left(k\in\mathbb{Z}\right)$ vertices exhibit…
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 $u,v$,…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using…