Related papers: Discrete-time quantum walk algorithm for ranking n…
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of…
This work revisits quantum algorithms for the well-known welded tree problem, proposing a very succinct quantum algorithm based on the simplest coined quantum walks. It simply iterates the naturally defined coined quantum walk operator for…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
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 walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum operations among quantum…
Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete…
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this…