Related papers: Quasi-Monte Carlo Method for Linear Combination Un…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling,…
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…
In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can…
We develop a GPU-accelerated hybrid quantum Monte Carlo (QMC) algorithm to solve the fundamental yet difficult problem of $U(1)$ gauge field coupled to fermions, which gives rise to a $U(1)$ Dirac spin liquid state under the description of…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the…
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…
We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems. We obtain our…
We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After…
We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations,…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It…
Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube $[0,1]^d$ or at isolated…
Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In…
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole…
Ground state properties of the Hubbard model are of fundamental importance to understand the mechanism of unconventional superconductivity in the high-T_c cuprates and other materials. One of the most powerful numerical methods for strongly…
Theoretical predictions in high energy physics are routinely provided in the form of Monte Carlo generators. Comparisons of predictions from different programs and/or different initialization set-ups are often necessary. MC-TESTER can be…