Related papers: On Applying the Lackadaisical Quantum Walk Algorit…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
We present a novel quantum walk-based approach to solve the Minimum Spanning Tree (MST) problem under a maximal degree constraint (MDC). By recasting the classical MST problem as a quantum walk on a graph, where vertices are encoded as…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
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…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
Chakraborty and Leonardo have shown that a spatial search by quantum walk is optimal for almost all graphs. However, we observed that on some graphs, certain states cannot be searched optimally. We present a method for constructing an…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged…
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…