Related papers: A duality at the heart of Gaussian boson sampling
Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study Boson sampling from general,…
We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main…
Multiphoton interference is at the very heart of quantum foundations and applications in quantum sensing and information processing. In particular, boson sampling experiments have the potential to demonstrate quantum computational supremacy…
We introduce a polynomial invariant of graphs on surfaces, $P_G$, generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result for $P_G$, analogous to the duality for the Tutte…
The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known…
We consider mixtures of $k\geq 2$ Gaussian components with unknown means and unknown covariance (identical for all components) that are well-separated, i.e., distinct components have statistical overlap at most $k^{-C}$ for a large enough…
Graph condensation reduces the size of large graphs while preserving performance, addressing the scalability challenges of Graph Neural Networks caused by computational inefficiencies on large datasets. Existing methods often rely on…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
We propose boson sampling from a system of coupled photons and Bose-Einstein condensed atoms placed inside a multi-mode cavity as a simulation process testing quantum advantage of quantum systems over classical computers. Consider a…
Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review,…
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…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…