Related papers: Implementation of Continuous-Time Quantum Walk on …
The continuous-time quantum walks (CTQWs) are a fundamental tool in the development of quantum algorithms. Recently, it was shown that discretizations of p-adic Schr\"odinger equations give rise to continuous-time quantum Markov chains…
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…
Open quantum walks (OQW) are formulated as quantum Markov chains on graphs. It is shown that OQWs are a very useful tool for the formulation of dissipative quantum computing algorithms and for dissipative quantum state preparation. In…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
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…
A fully connected vertex $w$ in a simple graph $G$ of order $N$ is a vertex connected to all the other $N-1$ vertices. Upon denoting by $L$ the Laplacian matrix of the graph, we prove that the continuous-time quantum walk (CTQW) -- with…
We investigate the quantum transport of delocalized states in continuous-time quantum walks (CTQWs) on a one-dimensional lattice containing a single defect. The defect is modeled by assigning complex-valued hopping amplitudes to the edges…
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…
In this work, we present a new model of the Discrete-Time Open Quantum Walk (DTOQW) applicable to an arbitrary graph, thereby going beyond the case of quantum walks on regular graphs. We study the impact of noise in the dynamics of quantum…
We study the dynamics of continuous-time quantum walks (CTQW) on networks with highly degenerate eigenvalue spectra of the corresponding connectivity matrices. In particular, we consider the two cases of a star graph and of a complete…
In a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). The method helps to reduce a graph into a simpler version that allows more…
Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. We introduce the phase quantum walk (PQW), a discrete-time quantum walk in which…
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…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…