Observations on variational and projector Monte Carlo methods

Umrigar, C. J.

doi:10.1063/1.4933112

Title: Observations on variational and projector Monte Carlo methods

Abstract

In this work, variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Lastly, approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.

Authors:

Umrigar, C. J. ^[1]

Cornell Univ., Ithaca, NY (United States). Laboratory of Atomic and Solid State Physics

Publication Date:: Mon Oct 26 00:00:00 EDT 2015

Research Org.:: Cornell Univ., Ithaca, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1469560

Alternate Identifier(s):: OSTI ID: 1224329

Grant/Contract Number:: SC0006650

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 143; Journal Issue: 16; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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                    Umrigar, C. J. Observations on variational and projector Monte Carlo methods.  United States: N. p., 2015. 
Web.  doi:10.1063/1.4933112.

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                    Umrigar, C. J. Observations on variational and projector Monte Carlo methods.  United States.  https://doi.org/10.1063/1.4933112

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                    Umrigar, C. J. Mon .  
"Observations on variational and projector Monte Carlo methods".  United States.  https://doi.org/10.1063/1.4933112.  https://www.osti.gov/servlets/purl/1469560.

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@article{osti_1469560,

  title        = {Observations on variational and projector Monte Carlo methods},

  author       = {Umrigar, C. J.},

  abstractNote = {In this work, variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Lastly, approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.},

  doi          = {10.1063/1.4933112},

  journal      = {Journal of Chemical Physics},

  number       = 16,

  volume       = 143,

  place        = {United States},

  year         = {Mon Oct 26 00:00:00 EDT 2015},

  month        = {Mon Oct 26 00:00:00 EDT 2015}

}

Copy to clipboard

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Quantum Monte Carlo method using phase-free random walks with Slater determinants
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Works referencing / citing this record:

Improved walker population control for full configuration interaction quantum Monte Carlo
journal, November 2020

Yang, Mingrui; Pahl, Elke; Brand, Joachim
The Journal of Chemical Physics, Vol. 153, Issue 17
DOI: 10.1063/5.0023088

Infinite Variance in Fermion Quantum Monte Carlo Calculations
text, January 2015

Shi, Hao; Zhang, Shiwei
arXiv
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Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
text, January 2017

Schwarz, Lauretta; Alavi, Ali; Booth, Gh
Apollo - University of Cambridge Repository
DOI: 10.17863/cam.11565

Ab-initio Quantum Monte Carlo study of ultracold atomic mixtures
preprint, January 2021

Cikojević, Viktor
arXiv
DOI: 10.48550/arxiv.2105.01439

Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo
text, January 2021

Brand, Joachim; Yang, Mingrui; Pahl, Elke
arXiv
DOI: 10.48550/arxiv.2103.07800

Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo
journal, January 2019

Otis, Leon; Neuscamman, Eric
Physical Chemistry Chemical Physics, Vol. 21, Issue 27
DOI: 10.1039/c9cp02269d

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
journal, April 2017

Schwarz, Lauretta R.; Alavi, A.; Booth, George H.
Physical Review Letters, Vol. 118, Issue 17
DOI: 10.1103/physrevlett.118.176403

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Similar Records

Title: Observations on variational and projector Monte Carlo methods

Abstract

Citation Formats

Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules journal, May 2008

Monte-Carlo solution of Schrödinger's equation journal, February 1971

Fermion Monte Carlo book, January 1999

Stable Liquid Hydrogen at High Pressure by a Novel Ab Initio Molecular-Dynamics Calculation journal, March 2008

Optimum and efficient sampling for variational quantum Monte Carlo text, January 2010

A diffusion Monte Carlo algorithm with very small time‐step errors journal, August 1993

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Quantum chemistry by random walk. H 2 P , H + 3 D 3 h 1 A ′ 1 , H 2 3 Σ + u , H 4 1 Σ + g , Be 1 S journal, November 1976

Quantum Monte Carlo simulations of solids journal, January 2001

Prospects for release-node quantum Monte Carlo journal, November 2011

Green Function Monte Carlo with Stochastic Reconfiguration journal, May 1998

Green’s function Monte Carlo for few fermion problems journal, December 1982

Released-phase quantum Monte Carlo method journal, May 1997

Fixed‐node quantum Monte Carlo for molecules a) b) journal, December 1982

Semistochastic Projector Monte Carlo Method journal, December 2012

The calculation of excited state properties with quantum Monte Carlo journal, November 1988

Monte Carlo methods null, January 1970

Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters journal, July 2001

Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states text, January 2013

An Exact Monte Carlo Method for Continuum Fermion Systems text, January 2000

Optimum and efficient sampling for variational quantum Monte Carlo journal, November 2010

Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods text, January 2007

Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions journal, March 2007

Equation of State Calculations by Fast Computing Machines journal, June 1953

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods journal, July 2007

Monte Carlo sampling methods using Markov chains and their applications journal, April 1970

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo journal, December 2014

Helium at zero temperature with hard-sphere and other forces journal, May 1974

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space journal, January 2009

Exact Monte Carlo calculation for few-electron systems journal, November 1991

Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants journal, April 2003

Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states journal, April 2013

Symmetry in auxiliary-field quantum Monte Carlo calculations journal, September 2013

Quantum Monte Carlo method using phase-free random walks with Slater determinants text, January 2002

Optimization of quantum Monte Carlo wave functions by energy minimization journal, February 2007

An auxiliary-field quantum Monte Carlo study of the chromium dimer journal, February 2015

Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems journal, July 2012

Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo journal, January 2010

Applications of quantum Monte Carlo methods in condensed systems journal, January 2011

Monte Carlo Methods in Ab Initio Quantum Chemistry book, March 1994

Diffusion Monte Carlo methods with a fixed number of walkers journal, April 2000

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions journal, May 1995

Energy and Variance Optimization of Many-Body Wave Functions journal, April 2005

A very high accuracy potential energy surface for H3 journal, January 1999

Ground State of the Electron Gas by a Stochastic Method journal, August 1980

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method journal, February 2012

Path integrals in the theory of condensed helium journal, April 1995

The Coupled Electronic-Ionic Monte Carlo Simulation Method book, January 2002

Quantum Many-Body Problems book, January 1979

Linear-scaling and parallelisable algorithms for stochastic quantum chemistry journal, January 2014

Towards an exact description of electronic wavefunctions in real solids journal, December 2012

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules text, January 2008

Quantum Monte Carlo for molecules: Green’s function and nodal release journal, December 1984

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo. journalarticle, January 2014

Effects of three-body and backflow correlations in the two-dimensional electron gas journal, October 1993

Alleviation of the Fermion-sign problem by optimization of many-body wave functions text, January 2006

Fermion Monte Carlo journal, September 1999

Improved walker population control for full configuration interaction quantum Monte Carlo journal, November 2020

Infinite Variance in Fermion Quantum Monte Carlo Calculations text, January 2015

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions text, January 2017

Ab-initio Quantum Monte Carlo study of ultracold atomic mixtures preprint, January 2021

Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo text, January 2021

Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo journal, January 2019

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions journal, April 2017

Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
journal, May 2008

Monte-Carlo solution of Schrödinger's equation
journal, February 1971

Fermion Monte Carlo
book, January 1999

Stable Liquid Hydrogen at High Pressure by a Novel Ab Initio Molecular-Dynamics Calculation
journal, March 2008

Optimum and efficient sampling for variational quantum Monte Carlo
text, January 2010

A diffusion Monte Carlo algorithm with very small time‐step errors
journal, August 1993

The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem
journal, January 2013

Quantum chemistry by random walk. H ² P , H ⁺ ₃ D _{3 h} ¹ A ′ ₁ , H ₂ ³ Σ ⁺ _u , H ₄ ¹ Σ ⁺ _g , Be ¹ S
journal, November 1976

Quantum Monte Carlo simulations of solids
journal, January 2001

Prospects for release-node quantum Monte Carlo
journal, November 2011

Green Function Monte Carlo with Stochastic Reconfiguration
journal, May 1998

Green’s function Monte Carlo for few fermion problems
journal, December 1982

Released-phase quantum Monte Carlo method
journal, May 1997

Fixed‐node quantum Monte Carlo for molecules ^a) b)
journal, December 1982

Semistochastic Projector Monte Carlo Method
journal, December 2012

The calculation of excited state properties with quantum Monte Carlo
journal, November 1988

Monte Carlo methods
null, January 1970

Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters
journal, July 2001

Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states
text, January 2013

An Exact Monte Carlo Method for Continuum Fermion Systems
text, January 2000

Optimum and efficient sampling for variational quantum Monte Carlo
journal, November 2010

Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
text, January 2007

Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions
journal, March 2007

Equation of State Calculations by Fast Computing Machines
journal, June 1953

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods
journal, July 2007

Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo
journal, December 2014

Helium at zero temperature with hard-sphere and other forces
journal, May 1974

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
journal, January 2009

Exact Monte Carlo calculation for few-electron systems
journal, November 1991

Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003

Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states
journal, April 2013

Symmetry in auxiliary-field quantum Monte Carlo calculations
journal, September 2013

Quantum Monte Carlo method using phase-free random walks with Slater determinants
text, January 2002

Optimization of quantum Monte Carlo wave functions by energy minimization
journal, February 2007

An auxiliary-field quantum Monte Carlo study of the chromium dimer
journal, February 2015

Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems
journal, July 2012

Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo
journal, January 2010

Applications of quantum Monte Carlo methods in condensed systems
journal, January 2011

Monte Carlo Methods in Ab Initio Quantum Chemistry
book, March 1994

Diffusion Monte Carlo methods with a fixed number of walkers
journal, April 2000

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
journal, May 1995

Energy and Variance Optimization of Many-Body Wave Functions
journal, April 2005

A very high accuracy potential energy surface for H3
journal, January 1999

Ground State of the Electron Gas by a Stochastic Method
journal, August 1980

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
journal, February 2012

Path integrals in the theory of condensed helium
journal, April 1995

The Coupled Electronic-Ionic Monte Carlo Simulation Method
book, January 2002

Quantum Many-Body Problems
book, January 1979

Linear-scaling and parallelisable algorithms for stochastic quantum chemistry
journal, January 2014

Towards an exact description of electronic wavefunctions in real solids
journal, December 2012

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
text, January 2008

Quantum Monte Carlo for molecules: Green’s function and nodal release
journal, December 1984

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo.
journalarticle, January 2014

Effects of three-body and backflow correlations in the two-dimensional electron gas
journal, October 1993

Alleviation of the Fermion-sign problem by optimization of many-body wave functions
text, January 2006

Fermion Monte Carlo
journal, September 1999

Improved walker population control for full configuration interaction quantum Monte Carlo
journal, November 2020

Infinite Variance in Fermion Quantum Monte Carlo Calculations
text, January 2015

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
text, January 2017

Ab-initio Quantum Monte Carlo study of ultracold atomic mixtures
preprint, January 2021

Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo
text, January 2021

Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo
journal, January 2019

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
journal, April 2017