Related papers: Point Processes with Gaussian Boson Sampling
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…
We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
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…
Boson is one of the most basic types of particles and preserves the commutation relation. An efficient way to measure a bosonic system is important not only for simulating complex physics phenomena of bosons (such as nuclei) on a qubit…
Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization.…
Sampling the distribution of bosons that have undergone a random unitary evolution is strongly believed to be a computationally hard problem. Key to outperforming classical simulations of this task is to increase both the number of input…
BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In arXiv:1306.3995, Gogolin et al. claimed that even an ideal…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…