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The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM)…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
Tensor network states have enjoyed great success at capturing aspects of strong correlation physics. However, obtaining dynamical correlators at non-zero temperatures is generically hard even using these methods. Here, we introduce a…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the…
Approximate Bayesian Computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…
We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for…
In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a…
A new algorithm for analytic continuation of noisy quantum Monte Carlo (QMC) data from the Matsubara domain to real frequencies is proposed. Unlike the widely used maximum-entropy (MaxEnt) procedure, our method is linear with respect to…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information…
This paper generalizes the (0+1)-dimensional spin-boson problem to the corresponding (1+1)-dimensional version. Monte Carlo simulation is used to find the phase diagram and imaginary time correlation function. The real frequency spectrum is…
We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin S. By quantum Monte Carlo simulation we compute this spectrum for the s=1/2, s=1 and s=3/2 Heisenberg models. We…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
We propose a new method to efficiently compute the entanglement entropy (EE) of quantum many-body systems. Our approach, called the incremental SWAP operator method , combines the simplicity of the SWAP operator used in projector quantum…
Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of…
By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg ($XXX$) chain. The key idea is to sample the…