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

Civil War Book Review

Sign Learning Kink based Quantum Monte Carlo Applied to Multiple Large Systems H2O, N2, F2

Ma, Xiaoyao

Published Jun 24, 2014• 0 citations
Publisher

Abstract

A Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ground state energies for H2O, N2 and F2 molecules. This method has two stages. The first (learning stage) reduces the minus sign problem by optimizing the states which are used in the second (QMC stage). I test the method in Single, Double excitations (SD), Single, Double, and Triple excitations (SDT), and Full Configuration Interaction (FCI) vector spaces. I also perform exact diagonalization in those vector spaces as a benchmark. In each vector space and for each molecule, I perform SiLK QMC for different bond lengths demonstrating that the SiLK QMC is applicable to many systems.

DOI
10.31390/gradschool_dissertations.1728

Related papers

Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems

Xiaoyao Ma, Randall W. Hall, Frank Löffler +4 more

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

arXiv:1512.05455•The Journal of Chemical Physics•Jan 5, 2016•0 citations

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC)

Xiaoyao Ma, Frank Löffler, Randall W. Hall +3 more

•Jan 1, 2015•0 citations

Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function

James J. Shepherd, Gustavo E. Scuseria, James S. Spencer

We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schr\"odinger equation with substantially reduced computational cost compared with exact diagonalization. We find $k$-space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of ${10}^{38}$ determinants) in 250 core hours, substantially quicker than the $\ensuremath{\sim}{10}^{36}$ core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.

arXiv:1407.4800•Physical Review B•Oct 27, 2014•35 citations

APPLYING QUANTUM MONTE CARLO TO THE ELECTRONIC STRUCTURE PROBLEM

Andrew Powell, Richard Dawes

Two distinct types of Quantum Monte Carlo (QMC) calculations are applied to electronic structure problems such as calculating potential energy curves and producing benchmark values for reaction barriers. First, Variational and Diffusion Monte Carlo (VMC and DMC) methods using a trial wavefunction subject to the fixed node approximation were tested using the CASINO code.[1] Next, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), along with its initiator extension (i-FCIQMC) were tested using the NECI code.[2] FCIQMC seeks the FCI energy for a specific basis set. At a reduced cost, the efficient i-FCIQMC method can be applied to systems in which the standard FCIQMC approach proves to be too costly. Since all of these methods are statistical approaches, uncertainties (error-bars) are introduced for each calculated energy. This study tests the performance of the methods relative to traditional quantum chemistry for some benchmark systems. References: [1] R. J. Needs et al., J. Phys.: Condensed Matter 22, 023201 (2010). [2] G. H. Booth et al., J. Chem. Phys. 131, 054106 (2009).

International Symposium on Molecular Spectroscopy (ISMS)•Jun 21, 2016•0 citations

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

Samuel M. Greene, Robert J. Webber, James E. T. Smith +2 more

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

arXiv:2201.12164•Journal of Chemical Theory and Computation•Nov 8, 2022•4 citations

Green's function quantum Monte Carlo method in the presence of topological sign problems: π electronic systems

Johannes Schütt, Michael C. Böhm

A Green's function quantum Monte Carlo (GF QMC) method is described which renders possible the determination of the exact ground state energy of any π system in the computational framework of effective π Hamiltonians. An instruction to evaluate the growth estimator in the simultaneous presence of positive and negative phases is suggested. Numerical results for five annulene molecules with 4–12 atomic centres as well as 10 further π molecules with different topology (i.e., monocycles with methylene groups, bi- and polycycles) are given. Negative phases occur in 13 of the 15 π networks considered. The statistical QMC results are compared with data derived by conventional (many-body) diagonalization techniques. The interaction-free Hückel Hamiltonian has been adopted as most simple setup to test the applicability of the Monte Carlo approach. Many-body results have been derived for the Hubbard and Pariser-Parr-Pople variants of the π-electron Hamiltonian. It is demonstrated that GF QMC results can be derived whose accuracy does not depend on the presence of negative signs in the numerical simulation.

Molecular Physics•Aug 20, 1995•10 citations
A Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ground state energies for H2O, N2 and F2 molecules. This method has two stages. The first (learning stage) reduces the minus sign problem by optimizing the states which are used in the second (QMC stage). I test the method in Single, Double excitations (SD), Single, Double, and Triple excitations (SDT), and Full Configuration Interaction (FCI) vector spaces. I also perform exact diagonalization in those vector spaces as a benchmark. In each vector space and for each molecule, I perform SiLK QMC for different bond lengths demonstrating that the SiLK QMC is applicable to many systems.
The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.
We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schr\"odinger equation with substantially reduced computational cost compared with exact diagonalization. We find kkk-space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of 1038{10}^{38}1038 determinants) in 250 core hours, substantially quicker than the $\ensuremath{\sim}{10}^{36}$ core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.
Two distinct types of Quantum Monte Carlo (QMC) calculations are applied to electronic structure problems such as calculating potential energy curves and producing benchmark values for reaction barriers. First, Variational and Diffusion Monte Carlo (VMC and DMC) methods using a trial wavefunction subject to the fixed node approximation were tested using the CASINO code.[1] Next, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), along with its initiator extension (i-FCIQMC) were tested using the NECI code.[2] FCIQMC seeks the FCI energy for a specific basis set. At a reduced cost, the efficient i-FCIQMC method can be applied to systems in which the standard FCIQMC approach proves to be too costly. Since all of these methods are statistical approaches, uncertainties (error-bars) are introduced for each calculated energy. This study tests the performance of the methods relative to traditional quantum chemistry for some benchmark systems. References: [1] R. J. Needs et al., J. Phys.: Condensed Matter 22, 023201 (2010). [2] G. H. Booth et al., J. Chem. Phys. 131, 054106 (2009).
We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.
A Green's function quantum Monte Carlo (GF QMC) method is described which renders possible the determination of the exact ground state energy of any π system in the computational framework of effective π Hamiltonians. An instruction to evaluate the growth estimator in the simultaneous presence of positive and negative phases is suggested. Numerical results for five annulene molecules with 4–12 atomic centres as well as 10 further π molecules with different topology (i.e., monocycles with methylene groups, bi- and polycycles) are given. Negative phases occur in 13 of the 15 π networks considered. The statistical QMC results are compared with data derived by conventional (many-body) diagonalization techniques. The interaction-free Hückel Hamiltonian has been adopted as most simple setup to test the applicability of the Monte Carlo approach. Many-body results have been derived for the Hubbard and Pariser-Parr-Pople variants of the π-electron Hamiltonian. It is demonstrated that GF QMC results can be derived whose accuracy does not depend on the presence of negative signs in the numerical simulation.