Adaptive Quantum Monte Carlo Approach States for High-Dimensional Systems

Venelin Todorov, Ivan Dimov

Jincheng Zhang

Quantum Monte Carlo (QMC) methods offer a powerful approach to solving complex quantum mechanical problems, particularly those with intricate constraints. However, traditional QMC implementations often struggle with the computational demands associated with handling these constraints effectively. This paper introduces a novel hybrid approach that integrates constraint mapping techniques directly into the Monte Carlo framework, aiming to significantly improve the efficiency and scalability of QMC for problems demanding robust constraint handling. We demonstrate the effectiveness of this integrated method through rigorous analysis and illustrative examples, addressing the limitations of current approaches and presenting a framework for tackling high-dimensional problems with inherent constraints. The core mechanism revolves around dynamically adapting constraint mappings during the Monte Carlo integration process, thereby reducing the computational burden and enhancing the algorithm's ability to navigate complex solution spaces.

Michael Dzierzawa, X. Zotos

James S. Spencer, Nick S. Blunt, Seonghoon Choi +15 more

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

Stephen Fahy

B. J. Alder, David M. Ceperley

The Monte Carlo method is a powerful scheme to solve many mathematical equations and is in fact, made practical only through high speed computers, particularly for those physical problems that are of high dimensionality. Alternative numerical schemes of spanning high dimensional spaces uniformly with a grid, increase in computational time exponentially with the dimensionality and thus became rapidly impractical as the dimensionality increases. The key to success of a Monte Carlo scheme is that it samples the space selectively, not with some uniform random distribution but where it matters most, by a probability density called an importance function. Furthermore, the Monte Carlo scheme is well adapted to computers since it consists of a simple, highly repetitive algorithm that takes advantage of the fast arithmetic capabilities of the machines. Consideration of how to arrange such calculations efficiently on various machines of different architecture is discussed.