Related papers: Determinant Monte Carlo algorithms for dynamical q…
Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
A two-dimensional lattice hard-core boson system with a small fraction of bosonic or fermionic impurity particles is studied. The impurities have the same hopping and interactions as the dominant bosons and their effects are solely due to…
Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
Piecewise Deterministic Monte Carlo algorithms enable simulation from a posterior distribution, whilst only needing to access a sub-sample of data at each iteration. We show how they can be implemented in settings where the parameters live…
The quantum Monte Carlo algorithm is arguably one of the most powerful computational many-body methods, enabling accurate calculation of many properties in interacting quantum systems. In the presence of the so-called sign problem, the…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
The increase with time of computer resources devoted to simulations of full QCD is spectacular. Yet the reduction of systematic errors is comparatively slow. This is due to the algorithmic complexity of the problem. I review, in elementary…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
We demonstrate the applicability of a recently proposed multiscale thermalization algorithm to two-color quantum chromodynamics (QCD) with two mass-degenerate fermion flavors. The algorithm involves refining an ensemble of gauge…
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing…
The performance of the Hybrid Monte Carlo algorithm is determined by the speed of sparse matrix-vector multiplication within the context of preconditioned conjugate gradient iteration. We study these operations as implemented for the…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…