Related papers: Zero Transfer in Continuous Time Quantum Walks
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
The effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a new model…
We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…
The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define…
A continuous-time quantum walk on a graph evolves according to the unitary operator $e^{-iAt}$, where $A$ is the adjacency matrix of the graph. Perfect state transfer (PST) in a quantum walk is the transfer of a quantum state from one node…
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…
It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as…
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…
We demonstrate that continuous time quantum walks on several types of branching graphs, including graphs with loops, are identical to quantum walks on simpler linear chain graphs. We also show graph types for which such equivalence does not…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of…
Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs however, can have…
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…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…
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…
Continuous-time quantum walks (CTQWs) play a crucial role in quantum computing, especially for designing quantum algorithms. However, how to efficiently implement CTQWs is a challenging issue. In this paper, we study implementation of CTQWs…