Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optimization of many-body wave functions: a route to systematic reduction of the diffusion Monte Carlo fixed-node error

Cyrus J. Umrigar, Julien Toulouse, Claudia Filippi, Sandro Sorella, Richard G. Hennig

Published Nov 3, 2006• 0 citations
OpenAlex

Related papers

Self-healing diffusion quantum Monte Carlo algorithms: Direct reduction of the fermion sign error in electronic structure calculations

Fernando Agustín Reboredo, Randolph Q. Hood, Paul R. C. Kent

We develop a formalism and present an algorithm for optimization of the trial wave function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground-state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project out a multideterminant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multideterminant expansions of the trial wave function. The method can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where benchmark configuration-interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal noninteracting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77, 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.

arXiv:0808.3417•Physical Review B•May 19, 2009•30 citations

Monte-Carlo solution to the many-body schrödinger equation

John G. Zabolitzky

Progress in Particle and Nuclear Physics•Jan 1, 1986•9 citations

Variational Optimization of Many-Body Wave Functions

Ryo Maezono

Springer eBooks•Nov 8, 2025•0 citations

Systematic reduction of sign errors in many-body problems: Generalization of self-healing diffusion Monte Carlo to excited states

Fernando Agustín Reboredo

A recently developed self-healing diffusion Monte Carlo algorithm [F. A. Reboredo, R. Q. Hood, and P. R. C. Kent, Phys. Rev. B 79, 195117 (2009)] is extended to the calculation of excited states. The formalism is based on an excited-state fixed-node approximation and the mixed estimator of the excited-state probability density. The fixed-node ground-state wave-functions of inequivalent nodal pockets are found simultaneously using a recursive approach. The decay of the wave-function into lower-energy states is prevented using two methods: (i) the projection of the improved trial-wave function into previously calculated eigenstates is removed; and (ii) the reference energy for each nodal pocket is adjusted in order to create a kink in the global fixed-node wave-function, which, when locally smoothed, increases the volume of the higher-energy pockets at the expense of the lower-energy ones until the energies of every pocket become equal. This reference energy method is designed to find nodal structures that are local minima for arbitrary fluctuations of the nodes within a given nodal topology. It is demonstrated in a model system that the algorithm converges to many-body eigenstates in bosonic and fermionic cases.

arXiv:0906.4359•Physical Review B•Sep 14, 2009•10 citations

Assessing orbital optimization in variational and diffusion Monte Carlo

Cody Melton, Jaron T. Krogel

In this work, we investigate whether the use of orbital optimization in variational Monte Carlo is able to systematically improve diffusion Monte Carlo results on correlated magnetic systems, using CrSBr as a model system. We show that short-range Jastrow factors are important for improving diffusion Monte Carlo, regardless of the quality of the orbitals. Large active spaces are required to converge the variational energy, but ultimately orbital optimization produces worse diffusion Monte Carlo energies when compared to standard orbitals from density functional theory. We show that this increased bias is due to larger locality errors from the use of pseudopotentials, while the fixed-node error is actually improved by using orbital optimization. In addition, for observables other than energy, orbital optimization produces a systematically smaller mixed-estimator bias. Ultimately, we believe that orbital optimization provides a reliable method for improving variational and pure fixed-node energies, as well as reducing mixed-estimator bias.

arXiv:2601.15169•The Journal of Chemical Physics•Apr 24, 2026•0 citations

Variational and Diffusion Monte Carlo Approaches to the Nuclear Few- and Many-Body Problem

Francesco Pederiva, Alessandro Roggero, Kevin E. Schmidt

Lecture notes in physics•Jan 1, 2017•7 citations
We develop a formalism and present an algorithm for optimization of the trial wave function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground-state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project out a multideterminant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multideterminant expansions of the trial wave function. The method can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where benchmark configuration-interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal noninteracting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77, 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
A recently developed self-healing diffusion Monte Carlo algorithm [F. A. Reboredo, R. Q. Hood, and P. R. C. Kent, Phys. Rev. B 79, 195117 (2009)] is extended to the calculation of excited states. The formalism is based on an excited-state fixed-node approximation and the mixed estimator of the excited-state probability density. The fixed-node ground-state wave-functions of inequivalent nodal pockets are found simultaneously using a recursive approach. The decay of the wave-function into lower-energy states is prevented using two methods: (i) the projection of the improved trial-wave function into previously calculated eigenstates is removed; and (ii) the reference energy for each nodal pocket is adjusted in order to create a kink in the global fixed-node wave-function, which, when locally smoothed, increases the volume of the higher-energy pockets at the expense of the lower-energy ones until the energies of every pocket become equal. This reference energy method is designed to find nodal structures that are local minima for arbitrary fluctuations of the nodes within a given nodal topology. It is demonstrated in a model system that the algorithm converges to many-body eigenstates in bosonic and fermionic cases.
In this work, we investigate whether the use of orbital optimization in variational Monte Carlo is able to systematically improve diffusion Monte Carlo results on correlated magnetic systems, using CrSBr as a model system. We show that short-range Jastrow factors are important for improving diffusion Monte Carlo, regardless of the quality of the orbitals. Large active spaces are required to converge the variational energy, but ultimately orbital optimization produces worse diffusion Monte Carlo energies when compared to standard orbitals from density functional theory. We show that this increased bias is due to larger locality errors from the use of pseudopotentials, while the fixed-node error is actually improved by using orbital optimization. In addition, for observables other than energy, orbital optimization produces a systematically smaller mixed-estimator bias. Ultimately, we believe that orbital optimization provides a reliable method for improving variational and pure fixed-node energies, as well as reducing mixed-estimator bias.