Related papers: Comparing classical and quantum PageRanks
This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…
We study the differential privacy (DP) of the quantum recommendation algorithm of Kerenidis--Prakash and its quantum-inspired classical counterpart. Under standard low-rank and incoherence assumptions on the preference matrix, we show that…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
In the past decade, several small-scale quantum key distribution networks have been established. However, the deployment of large-scale quantum networks depends on the development of quantum repeaters, quantum channels, quantum memories,…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
A modification of Tulsi's quantum search algorithm with intermediate measurements of the control is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…
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…
A recent paper on quantum walks by Childs et al. [STOC'03] provides an example of a black-box problem for which there is a quantum algorithm with exponential speedup over the best classical randomized algorithm for the problem, but where…
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…
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…