相关论文: Quantum walks on Cayley graphs
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group $\mathbb Z^3$, that in an appropriate regime evolves…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…