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SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives:…
We investigate the use of randomized quasi-Monte Carlo (RQMC) in walk on spheres algorithms to solve boundary value problems for functions with Dirichlet boundary conditions in $\mathbb{R}^d$. For harmonic functions with $d=2$, the…
We study the fair sampling properties of hybrid quantum-classical Markov chain Monte Carlo (MCMC) algorithms for combinatorial optimization problems with degenerate ground states. While quantum optimization heuristics such as quantum…
We propose a technique to effectively sample initial neutron and delayed neutron precursor particles for Monte Carlo (MC) simulations of typical off-critical reactor transients. The technique can be seen as an improvement, or alternative,…
Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the last decade. The full configuration interaction quantum…
We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…
The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because…
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
Phonon Monte Carlo (PMC) is a versatile stochasic technique for solving the Boltzmann transport equation for phonons. It is particularly well suited for analyzing thermal transport in structures that have real-space roughness or are too…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
An iterative version of the qubit coupled cluster (QCC) method [I.G. Ryabinkin et al., J. Chem. Theory Comput. 14, 6317 (2019)] is proposed. The new method seeks to find ground electronic energies of molecules on noisy intermediate-scale…
We introduce a new algorithm which we call the {Rational Hybrid Monte Carlo} Algorithm (RHMC). This method uses a rational approximation to the fermionic kernel together with a noisy Kennedy-Kuti acceptance step to give an efficient…
We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and…
We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…
Deep learning methods have achieved great success in solving partial differential equations (PDEs), where the loss is often defined as an integral. The accuracy and efficiency of these algorithms depend greatly on the quadrature method. We…