Related papers: One Dimensional Quantum Walks with Two-step Memory
In this expository note, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
Quantum measurements play a fundamental role in quantum mechanics and quantum information processing, but it is not easy to implement generalized measurements, the most powerful measurements allowed by quantum mechanics. Here we propose a…
We address multi-parameter quantum estimation for one-dimensional discrete-time quantum walks and its applications to quantum metrology. We use the quantum walker as a probe for unknown parameters encoded on its coin degrees of freedom. We…
This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new technique which allow us to use a spectral mapping theorem for…
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm -- a quantum algorithm solving systems of linear equations -- in solving an open problem about quantum random walks, namely computing hitting (or absorption)…
We put forward a new, versatile and highly-scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small…
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
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…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…
A simple coined quantum walk in one dimension can be characterized by a $SU(2)$ operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In…