Related papers: The Wigner branching random walk: Efficient implem…
The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high…
We prove that a quantum walk can detect the presence of a marked element in a graph in $O(\sqrt{WR})$ steps for any initial probability distribution on vertices. Here, $W$ is the total weight of the graph, and $R$ is the effective…
We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the…
The density of states of continuous models is known to span many orders of magnitudes at different energies due to the small volume of phase space near the ground state. Consequently, the traditional Wang-Landau sampling which uses the same…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
We introduce a model of interacting random walkers on a finite one dimensional chain with absorbing boundaries or targets at the ends. Walkers are of two types: informed particles that move ballistically towards a given target, and…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…