Related papers: Neural Autoregressive Control Variates for the Qua…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…
The notorious sign problem severely limits the applicability of quantum Monte Carlo (QMC) simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…
Quantum Monte Carlo (QMC) methods for the frustrated quantum spin systems occasionally suffer from the negative sign problem, which makes simulations exponentially harder for larger systems at lower temperatures and severely limits QMC's…
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in…
We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand…
Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…
This paper presents a method to leverage arbitrary neural network architecture for control variates. Control variates are crucial in reducing the variance of Monte Carlo integration, but they hinge on finding a function that both correlates…
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…
We present a new Monte Carlo algorithm for simulating quantum spin systems which is able to suppress the negative sign problem. This algorithm has only a linear complexity in the lattice size used for the simulation. A general description…
We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as…
Black-box variational inference performance is sometimes hindered by the use of gradient estimators with high variance. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. While existing control…
Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically…
The sign problem in quantum Monte Carlo calculations is analyzed using the meron-cluster solution. The concept of merons can be used to solve the sign problem for a limited class of models. Here we show that the method can be used to…
Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the…
Lattice Monte Carlo calculations of interacting systems on non-bipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to…
Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation…