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We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on…
Link prediction is one of the fundamental problems in graph theory, critical for understanding and forecasting the evolution of complex systems like social and biological networks. While classical heuristics capture certain aspects of graph…
The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement…
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in $2$D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant…
We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of…
Deterministic tourist walk (DTW) has attracted increasing interest in computer vision. In the last years, different methods for analysis of dynamic and static textures were proposed. So far, all works based on the DTW for texture analysis…
History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of…
In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the…
Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular…
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 introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…
We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural…
Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…
A second-order random walk on a graph or network is a random walk where transition probabilities depend not only on the present node but also on the previous one. A notable example is the non-backtracking random walk, where the walker is…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
We consider the problem of the first passage time to the origin of a spatially non-homogeneous random walk with a position-dependent drift, known as the Gillis random walk, in the presence of resetting. The walk starts from an initial site…
In this work, we study the dynamics of multiple random walkers on networks subject to a simultaneous resetting protocol, whereby all walkers are synchronously returned to their respective initial nodes. For this collective Markovian…