Related papers: On the equivalence between quantum and random walk…
The utilization of quantum entanglement as a cryptographic resource has superseded conventional approaches to secure communication. Security and fidelity of intranetwork communication between quantum devices is the backbone of a quantum…
Currently there are three major paradigms of quantum computation, the gate model, annealing, and walks on graphs. The gate model and quantum walks on graphs are universal computation models, while annealing plays within a specific subset of…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
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…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…
Let $X$ be a graph with adjacency matrix $A$. The \textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\in V(X)$, then \[1-|U(t)_{a,a}|\le2/n. \] In a…
It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…
In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for $N$-fold star power graph, which are invariant under the quantum…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…