Related papers: Monte Carlo sampling from the quantum state space.…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of…
Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…
Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a…
For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The…