In this work we discuss several key aspects for an efficient implementation and deployment of large-scale quantum Monte Carlo (QMC) simulations for chemical applications on petaflops infrastructures. Such aspects have been implemented in the QMC=Chem code developed at Toulouse (France). First, a simple, general, and fault-tolerant simulation environment adapted to QMC algorithms is presented. S...

We review and apply quasi-Monte Carlo (QMC) and global sensitivity analysis (GSA) techniques to pricing and risk management (Greeks) of representative financial instruments of increasing complexity. We compare QMC vs. standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol’ low-discrepancy sequences, different discretization methods, and specific analyses of convergence,...

In many applications Monte Carlo (MC) sequences or Quasi-Monte Carlo (QMC) sequences are used for numerical integration. In moderate dimensions the QMC method typically yield better results, but its performance significantly falls off in quality if the dimension increases. One class of randomized QMC sequences, which try to combine the advantages of MC and QMC, are so-called mixed sequences, wh...

We present a new approach for Monte Carlo simulations of quantum spin systems which is able to strongly reduce the negative sign problem. Its efficiency is tested on a simple 2-dimensional fermionic model for which we show that our algorithm eliminates the sign problem. The investigation of quantum spin systems is important for understanding the physics related to strongly correlated electrons ...

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use Quasi-Monte Carlo (QMC) approximations inst...

The variational Monte Carlo method is reviewed here. It is in essence a classical statistical mechanics approach, yet allows the calculation of quantum expectation values. We give an introductory exposition of the theoretical basis of the approach, including sampling methods and acceleration techniques; its connection with trial wavefunctions; and how in practice it is used to obtain high quali...

The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical doping) are varied. Because of the strong coupling nature of this critical point and the "sign problem" plaguing numerical quantum Monte Carlo (QMC) methods, i...

The length of equal minimal and maximal blocks has eected on logarithm-scale logarithm against sequential function on variance and bias of de-trended uctuation analysis, by using Quasi Monte Carlo(QMC) simulation and Cholesky decompositions, minimal block couple and maximal are founded which are minimum the summation of mean error square in Horest power.

For many kinds of problem the accuracy of quantum Monte Carlo (QMC) is much better than that of density functional theory (DFT), and its scaling with number of atoms is much more favourable than that of high-level quantum chemistry. However, the widespread use of QMC has been hindered by the fact that it is considerably more expensive than DFT. We show here that QMC is very well placed to explo...

For many kinds of problem the accuracy of quantum Monte Carlo (QMC) is much better than that of density functional theory (DFT), and its scaling with number of atoms is much more favourable than that of high-level quantum chemistry. However, the widespread use of QMC has been hindered by the fact that it is considerably more expensive than DFT. We show here that QMC is very well placed to explo...