Related papers: The Wigner branching random walk: Efficient implem…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting…
In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of…
We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…
Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle…
A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, whereas its location on the Bloch sphere is described by the spin…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate…
Efficient inference of Deep Neural Networks (DNNs) is essential to making AI ubiquitous. Two important algorithmic techniques have shown promise for enabling efficient inference - sparsity and binarization. These techniques translate into…
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
In recent years, there has been an emerging trend of combining two innovations in computer science and physics to achieve better computation capability. Exploring the potential of quantum computation to achieve highly efficient performance…
Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…
It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space…
This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained problems and problems with non-binary variables. The algorithm returns optimal…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the…
The edge-reinforced random walk (ERRW) is a random process on the vertices of a graph that is more likely to cross the edges it has visited in the past. Depending on the strength of the reinforcement, the ERRW of a single particle can…