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Accelerating Markov Chain Monte Carlo Sampling With Diffusion Models, N. T. Hunt-Smith, W. Melnitchouk, F. Ringer, N. Sato, A. W. Thomas, M. J. White
Accelerating Markov Chain Monte Carlo Sampling With Diffusion Models, N. T. Hunt-Smith, W. Melnitchouk, F. Ringer, N. Sato, A. W. Thomas, M. J. White
Physics Faculty Publications
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the …
Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson
Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson
Physics Faculty Publications
We formulate the O(3) nonlinear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We …