Related papers: Quantum walks of interacting fermions on a cycle g…
Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
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 extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
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…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
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…
The dynamics of a discrete-time quantum walk (DTQW) can be realized within a purely classical interacting particle system composed of some boxes and a large but finite number of balls, and can, in principle, be implemented in a tabletop…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…