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We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we…

We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…

Numerical Analysis · Mathematics 2020-12-09 Benedict Leimkuhler , Matthias Sachs

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…

Probability · Mathematics 2015-02-20 Luc Rey-Bellet , Konstantinos Spiliopoulos

A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…

Quantum Physics · Physics 2015-06-03 A. Ramezanpour

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

Machine Learning · Statistics 2022-07-26 Michael Y. -S. Fang , Mayur Mudigonda , Ryan Zarcone , Amir Khosrowshahi , Bruno A. Olshausen

We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…

Numerical Analysis · Mathematics 2022-01-25 Giacomo Garegnani , Andrea Zanoni

Sampling from lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, the classic Gibbs algorithm from Markov chain Monte Carlo (MCMC) methods is demonstrated to be…

Information Theory · Computer Science 2018-12-03 Zheng Wang

We study a number of filtering schemes for the reduction of the statistical error in non-adiabatic calculations by means of the quantum-classical Liouville equation. In particular, we focus on a scheme based on setting a threshold value on…

Quantum Physics · Physics 2016-10-21 Daniel Uken , Alessandro Sergi , Francesco Petruccione

This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…

Analysis of PDEs · Mathematics 2021-12-16 Gabriel Stoltz

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…

Statistical Mechanics · Physics 2018-01-23 Jakub Ślęzak , Ralf Metzler , Marcin Magdziarz

Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…

Quantum Physics · Physics 2025-06-10 Longyun Chen , Jingcheng Liu , Penghui Yao

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

Optimization and Control · Mathematics 2024-10-29 Xinzhe Zuo , Stanley Osher , Wuchen Li

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…

This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…

Machine Learning · Statistics 2025-01-08 Luiz F. O. Chamon , Mohammad Reza Karimi , Anna Korba

We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…

Optimization and Control · Mathematics 2020-04-03 Adel Bibi , El Houcine Bergou , Ozan Sener , Bernard Ghanem , Peter Richtárik

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…

Computation · Statistics 2016-04-20 Francois Septier , Gareth W. Peters

Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed…

Mathematical Physics · Physics 2011-03-31 Anders Szepessy

We apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for community…

Quantum Physics · Physics 2022-03-15 Chris Cade , Marten Folkertsma , Ido Niesen , Jordi Weggemans

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Machine Learning · Statistics 2017-03-01 Pan Xu , Jian Ma , Quanquan Gu

Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address…

Computation · Statistics 2023-05-04 Marcelo Pereyra , Luis A. Vargas-Mieles , Konstantinos C. Zygalakis