Related papers: Quantum walks in the density operator picture
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
A discrete-time staggered quantum walk was recently introduced as a generalization that allows to unify other versions, such as the coined and Szegedy's walk. However, it also produces new forms of quantum walks not covered by previous…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…
The discrete-time quantum walk (QW) has been extensively and intensively investigated for the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. To this end, a constructive approach is employed by introducing a localized and a delocalized basis for the…
We define and analyze random quantum walks on homogeneous trees of degree $q\geq 3$. Such walks describe the discrete time evolution of a quantum particle with internal degree of freedom in $\C^q$ hopping on the neighboring sites of the…
Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an…
We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
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…
We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain…