Related papers: A Multigrid Algorithm for Sampling Imaginary-Time …
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin…
Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Simulations of QCD suffer from severe critical slowing down towards the continuum limit. This problem is known to be prominent in the topological charge, however, all observables are affected to various degree by these slow modes in the…
The wave-function Monte-Carlo method, also referred to as the use of "quantum-jump trajectories", allows efficient simulation of open systems by independently tracking the evolution of many pure-state "trajectories". This method is ideally…
Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique…
Sampling problems are widely regarded as the task for which quantum computers can most readily provide a quantum advantage. Leveraging this feature, the quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287…
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is…
We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. We consider in detail one-spin facilitated models, such as the East model and its generalizations to…
We consider Monte Carlo simulations of classical spin models of statistical mechanics using the massively parallel architecture provided by graphics processing units (GPUs). We discuss simulations of models with discrete and continuous…
Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science, and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum…
We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$…
Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from…