Related papers: Non-Markovianity in Discrete-Time Open Quantum Ran…
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…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schr\"{o}dinger equation. We show in two ways that our DTQW is…
We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…
The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties…
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…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader…
We present various results on the scheme introduced , which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field…
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…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in…
Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…
Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum…
Quantum walks are a powerful framework for the development of quantum algorithms, with lackadaisical quantum walks (LQWs) standing out as an efficient model for spatial search. In this work, we investigate how broken-link decoherence…
Discrete-time quantum walk (DTQW) represents a convenient mathematical framework for describing the motion of a particle on a discrete set of positions when this motion is conditioned by the values of certain internal degrees of freedom,…
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always…
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…