Related papers: Sampling unitary invariant ensembles
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Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains…
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We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
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Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1 - J_2$ model. The…
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Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
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High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda_i\}$ and eigenvectors $\{{\bf u}_i\}$ of a covariance matrix are central to such endeavors,…
This paper is a tutorial and literature review on sampling algorithms. We have two main types of sampling in statistics. The first type is survey sampling which draws samples from a set or population. The second type is sampling from…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…