Optimum scaling in a Monte Carlo method for quantum chemistry

Brenda M. Rubenstein

Tianchen Zhao

The variational quantum Monte Carlo (VQMC) method has received significant attention because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems, by representing the exponentially complex quantum states variationally with machine learning models. We develop novel training strategies to improve the scalability of VQMC, and build parallelization frameworks for solving large-scale problems. The application of our method is extended to quantum chemistry and financial derivative pricing. For quantum chemistry, we build a pre-processing pipeline serving as an interface connecting molecular information and VQMC, and achieve remarkable performance in comparison with the classical approximate methods. On the other hand, we present a simple generalization of VQMC applicable to arbitrary linear PDEs, showcasing the technique in the Black-Scholes equation for pricing European contingent claims dependent on many underlying assets. We also introduce meta-learning and multi-fidelity active learning as exotic components to VQMC, which, under some reasonable assumptions on the problem formulation, can further improve the convergence and the sampling efficiency of our method.

Michel Caffarel, Carlo, UK +2 more

Kevin E. Gasperich

Quantum chemistry is a useful tool that provides insight into the properties and behavior of chemical systems. Modern software packages have made quantum chemistry methods more easily accessible, and the continued increase in available computational resources has allowed them to be applied to larger systems at higher levels of theory. Two significant problems that the field faces are the high computational complexity of high-level methods and the shift toward parallelism in high performance computing architectures. This work examines the treatment of weakly interacting molecular systems with the fixed-node diffusion Monte Carlo (DMC) method. DMC and other quantum Monte Carlo (QMC) methods offer a possible solution to both of the aforementioned problems: they can produce near-exact results with a lower scaling (with respect to problem size) than other similarly-accurate methods, and they are inherently parallel, so there is little additional cost associated with distributing the work of a single QMC calculation across a large number of processing units. The only error in DMC that is not systematically improvable is the constraint of a fixed nodal surface of the many-particle wave function of the system being studied. There are many cases in which a single Slater determinant trial function is sufficient to obtain accurate results, but there are others in which more sophisticated multi-determinant trial functions are necessary. Furthermore, it is non-trivial to generate nodal surfaces of similar quality for isolated and interacting molecules, so cancellation of errors is not guaranteed. We examine the use of different single- and multi-determinant trial functions in DMC calculations on small chemical systems with the goal of further understanding how to construct appropriate trial functions for molecules and clusters.

H. DeRaedt, Ad Lagendijk, Pedro de Vries