Related papers: Estimation of one-dimensional discrete-time quantu…
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…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a…
We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state nuclear magnetic resonance for machine learning. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and…
We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to…
The properties of the coinless quantum walk model have not been as thoroughly analyzed as those of the coined model. Both evolve in discrete time steps but the former uses a smaller Hilbert space, which is spanned merely by the site basis.…
We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…
Here we present neutrino oscillation in the frame-work of quantum walks. Starting from a one spatial dimensional discrete-time quantum walk we present a scheme of evolutions that will simulate neutrino oscillation. The set of quantum walk…
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.…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
This paper examines a way to simplify the circuit of quantum random walk search algorithm, when the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier. If an appropriate relation…
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…
We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Using methods originally developed for "electric" walks with a…
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…