Improvement of a quantum monte carlo method

M. Ulmke, H. M�ller-Krumbhaar

Stephen Fahy

黄宏新

In this paper, a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self-optimizing and self-improving procedure. In contrast to the previous EFN-QMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not be-fore beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent tech-nique is used, in which the step size is automatically adjustable.The procedure is quasi-Newton type and converges super linear-ly. The present method also uses a novel trial function, which has correct electron-electron and electron-nucleus cusp condi-tious. The novel EFNQMC algorithm and the novel trial func-tion are employed to calculate the energies of 1 ^1A1 state of CH2, ^1Ag state of Cs and the ground-states of H2, LiH, Li2 and H2O.

Sebastian Manten, Arne Lüchow

The scaling of the diffusion quantum Monte Carlo method can be greatly improved when localized orbitals and short-range correlation functions are employed as recently suggested by the authors. The local diffusion quantum Monte Carlo method is described in detail with a careful analysis of errors. The new method achieves near linear scaling in the calculation of the local energy. Results demonstrating the improved performance are presented.

Michael Dzierzawa, X. Zotos

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.