Quantum Monte Carlo Programming

Lynne Serré

The Monte Carlo method uses a random sample of size n to approximate the value of an s-dimensional integral and has a convergence rate of O(n−1/2). By using lowdiscrepancy sampling, the quasi-Monte Carlo (QMC) method achieves a convergence rate of O(n−1(log n)), which is asymptotically faster than that of the Monte Carlo method. However, due to the dependence of the QMC error bound on the dimension s, this result doesn’t hold at practical values of n for even relatively small values of s. Still, many empirical studies have shown that QMC can outperform Monte Carlo integration in highdimensional problems at practical values of n. Empirical studies are often conducted by researchers to investigate the behaviour of QMC methods since the QMC error bound suffers from several practical limitations. This paper presents a Matlab program that implements some of the more commonly used numerical tests and provides a simple graphical summary of the results.

Osama M. Raisuddin, Suvranu De

Douglas J. Scalapino

Anthony Scemama, Michel Caffarel, Emmanuel Oseret +1 more

Luboš Mitáš

E. Slootman, Vijay Gopal Chilkuri, Aurélien Delval +16 more

Quantum Monte Carlo (QMC) methods deliver highly accurate electronic structure calculations but are computationally intensive. The quantum Monte Carlo kernel library (QMCkl) provides a modular, portable collection of high-performance kernels implementing the core building blocks of QMC calculations. It offers a C-compatible application programming interface, supports the TREXIO standard for input, and covers essential QMC kernels including atomic and molecular orbitals, cusp corrections, the Jastrow factor, and the necessary derivatives also to perform variational and structural optimization. QMCkl separates algorithmic development from hardware-specific tuning by combining human-readable reference implementations with performance-optimized kernels that produce identical numerical results. The library enables consistent, efficient, and reproducible simulations across different QMC codes and architectures and achieves substantial speedups in the evaluation of the energy and its derivatives. Beyond QMC, QMCkl can accelerate deterministic quantum chemistry workflows and visualization tools, promoting cross-code interoperability and simplifying high-performance scientific software development.