Related papers: Google In A Photonic Lattice
Google's PageRank has created a new synergy to information retrieval for a better ranking of Web pages. It ranks documents depending on the topology of the graphs and the weights of the nodes. PageRank has significantly advanced the field…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
We study the localization properties of eigenvectors of the Google matrix, generated both from the World Wide Web and from the Albert-Barabasi model of networks. We establish the emergence of a delocalization phase for the PageRank vector…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
On the case that the number of dangling nodes is large, PageRank computation can be proceeded with a much smaller matrix through lumping all dangling nodes of a web graph into a single node. Thus, it saves many computational cost and…
PageRank for Semi-Supervised Learning has shown to leverage data structures and limited tagged examples to yield meaningful classification. Despite successes, classification performance can still be improved, particularly in cases of fuzzy…
In this paper we consider so-called Google matrices and show that all eigenvalues ($\lambda$) of them have a fundamental property $|\lambda|\leq 1$. The stochastic eigenvector corresponding to $\lambda=1$ called the PageRank vector plays a…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable…
A particle-swarm is a set of indivisible processing elements that traverse a network in order to perform a distributed function. This paper will describe a particular implementation of a particle-swarm that can simulate the behavior of the…
The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent…
Search services have been developed rapidly in social Internet. It can help web users easily to find their documents. So that, finding a best method search is always an imagine. This paper would like introduce hybrid method of LPageRank…
Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the…
A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a…