Related papers: Quantum walks on two-dimensional grids with multip…
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…
Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…
We present various results on the scheme introduced , which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field…
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…
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.…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
Recently several quantum search algorithms based on quantum walks were proposed. Those algorithms differ from Grover's algorithm in many aspects. The goal is to find a marked vertex in a graph faster than classical algorithms. Since the…
The quantum walk differs fundamentally from the classical random walk in a number of ways, including its linear spreading and initial condition dependent asymmetries. Using stationary phase approximations, precise asymptotics have been…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
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…