Related papers: Analyzing Boltzmann Samplers for Bose-Einstein Con…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
The number of atoms in Bose-Einstein condensate determines the scale of experiments that can be performed, making it crucial for quantum simulations. Optimization of the number of atoms in the condensate is a complex problem which could be…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
This paper presents a novel algorithm solving the classic problem of generating a random sample of size s from population of size n with non-uniform probabilities. The sampling is done with replacement. The algorithm requires constant…
The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the random material is chosen - the representative volume - and its…
We derive the projection hypothesis in projective quantum measurement by restricting the set of observables. This projection hypothesis accompanies a bipartite system with the von Neumann-type interaction, which consists of a quantum…
We show that powersets over structures with a bounded counting sequence can be sampled efficiently without evaluating the generating function. An algorithm is provided, implemented, and tested. Runtimes are comparable to existing Boltzmann…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
The Bouncy Particle Sampler is a novel rejection-free non-reversible sampler for differentiable probability distributions over continuous variables. We generalize the algorithm to piecewise differentiable distributions and apply it to…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
We theoretically examine photoassociation of a non-ideal Bose-Einstein condensate, focusing on evidence for a macroscopic superposition of atoms and molecules. This problem raises an interest because, rather than two states of a given…
Molecules are created from a Bose-Einstein condensate of atomic 87Rb using a Feshbach resonance. A Stern-Gerlach field is applied, in order to spatially separate the molecules from the remaining atoms. For detection, the molecules are…
Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often…
We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed…
We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to…