Related papers: Efficient Monte Carlo characterization of quantum …
In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In…
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
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…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schr\"odinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
I consider the problem of integrating a function $f$ over the $d$-dimensional unit cube. I describe a multilevel Monte Carlo method that estimates the integral with variance at most $\epsilon^{2}$ in $O(d+\ln(d)d_{t}\epsilon^{-2})$ time,…
Quantum Monte Carlo methods are used to calculate various ground state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at $r_s\simeq…
Trading fidelity for scale enables approximate classical simulators such as matrix product states (MPS) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $\chi$ for MPS, governs the allocated…
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, Quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a…
Overlap between two neural quantum states can be computed through Monte Carlo sampling by evaluating the unnormalized probability amplitudes on a subset of basis configurations. Due to the presence of probability amplitude ratios in the…