skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms

Abstract

In this paper we outline the extension of recently introduced the sub-system embedding sub- algebras coupled cluster (SES-CC) formalism to the unitary CC formalism. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dy- namical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC formalism (DUCC) the corresponding CAS eigenvalue problem provides a rigorous sep- aration of external cluster amplitudes that describe dynamical correlation effects – used to define the effective Hamiltonian – from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of complete active space representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal targetmore » for several types of full configuration interaction (FCI) type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [2];  [2];  [2]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [1]
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States). William R. Wiley Environmental Molecular Sciences Lab.
  2. Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Quantum Information Science (QIS)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1574813
Alternate Identifier(s):
OSTI ID: 1530913; OSTI ID: 1598634
Report Number(s):
PNNL-SA-141041
Journal ID: ISSN 0021-9606; TRN: US2001250
Grant/Contract Number:  
AC05-76RL01830
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 1; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Quantum Information Science (QIS); ab initio, coupled-cluster, quantum chemistry, quantum computing

Citation Formats

Bauman, Nicholas P., Bylaska, Eric J., Krishnamoorthy, Sriram, Low, Guang Hao, Wiebe, Nathan, Granade, Christopher E., Roetteler, Martin, Troyer, Matthias, and Kowalski, Karol. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. United States: N. p., 2019. Web. doi:10.1063/1.5094643.
Bauman, Nicholas P., Bylaska, Eric J., Krishnamoorthy, Sriram, Low, Guang Hao, Wiebe, Nathan, Granade, Christopher E., Roetteler, Martin, Troyer, Matthias, & Kowalski, Karol. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. United States. doi:10.1063/1.5094643.
Bauman, Nicholas P., Bylaska, Eric J., Krishnamoorthy, Sriram, Low, Guang Hao, Wiebe, Nathan, Granade, Christopher E., Roetteler, Martin, Troyer, Matthias, and Kowalski, Karol. Wed . "Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms". United States. doi:10.1063/1.5094643. https://www.osti.gov/servlets/purl/1574813.
@article{osti_1574813,
title = {Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms},
author = {Bauman, Nicholas P. and Bylaska, Eric J. and Krishnamoorthy, Sriram and Low, Guang Hao and Wiebe, Nathan and Granade, Christopher E. and Roetteler, Martin and Troyer, Matthias and Kowalski, Karol},
abstractNote = {In this paper we outline the extension of recently introduced the sub-system embedding sub- algebras coupled cluster (SES-CC) formalism to the unitary CC formalism. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dy- namical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC formalism (DUCC) the corresponding CAS eigenvalue problem provides a rigorous sep- aration of external cluster amplitudes that describe dynamical correlation effects – used to define the effective Hamiltonian – from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of complete active space representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction (FCI) type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing.},
doi = {10.1063/1.5094643},
journal = {Journal of Chemical Physics},
number = 1,
volume = 151,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Coupled-cluster approach to nuclear physics
journal, May 2004


Error analysis and improvements of coupled-cluster theory
journal, January 1991


Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations
journal, January 1991

  • Kucharski, Stanislaw A.; Bartlett, Rodney J.
  • Theoretica Chimica Acta, Vol. 80, Issue 4-5
  • DOI: 10.1007/bf01117419

Application of Hilbert-space coupled-cluster theory to simple ( H 2 ) 2 model systems: Planar models
journal, April 1993


A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982

  • Purvis, George D.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 76, Issue 4
  • DOI: 10.1063/1.443164

Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
journal, February 2017


Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
journal, December 2006

  • Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard
  • Communications in Mathematical Physics, Vol. 270, Issue 2
  • DOI: 10.1007/s00220-006-0150-x

Multireference second-order perturbation theory: How size consistent is “almost size consistent”
journal, January 2005

  • Rintelman, Jamie M.; Adamovic, Ivana; Varganov, Sergey
  • The Journal of Chemical Physics, Vol. 122, Issue 4
  • DOI: 10.1063/1.1817891

The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt
journal, July 2001

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 115, Issue 2
  • DOI: 10.1063/1.1378323

Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
journal, April 2016

  • Schriber, Jeffrey B.; Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 144, Issue 16
  • DOI: 10.1063/1.4948308

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N 2 , C 2 , and Be 2
journal, September 2015

  • Bytautas, Laimutis; Scuseria, Gustavo E.; Ruedenberg, Klaus
  • The Journal of Chemical Physics, Vol. 143, Issue 9
  • DOI: 10.1063/1.4929904

A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces
journal, June 2018

  • Guo, Sheng; Li, Zhendong; Chan, Garnet Kin-Lic
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 8
  • DOI: 10.1021/acs.jctc.8b00273

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory
journal, January 2010

  • Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric
  • The Journal of Chemical Physics, Vol. 132, Issue 2
  • DOI: 10.1063/1.3275806

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene ?-electron models
journal, April 1992

  • Paldus, J.; Piecuch, P.
  • International Journal of Quantum Chemistry, Vol. 42, Issue 1
  • DOI: 10.1002/qua.560420110

Active-space coupled-cluster methods
journal, November 2010


Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
journal, November 2018

  • Lee, Joonho; Huggins, William J.; Head-Gordon, Martin
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b01004

Communication: Approaching exact quantum chemistry by cluster analysis of full configuration interaction quantum Monte Carlo wave functions
journal, October 2018

  • Deustua, J. Emiliano; Magoulas, Ilias; Shen, Jun
  • The Journal of Chemical Physics, Vol. 149, Issue 15
  • DOI: 10.1063/1.5055769

The density-matrix renormalization group
journal, April 2005


Canonical Configurational Interaction Procedure
journal, April 1960


Structure of Ni 78 from First-Principles Computations
journal, October 2016


The Fock space coupled cluster method: theory and application
journal, January 1991


Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations
journal, August 2017


Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal
journal, June 2014

  • Boguslawski, Katharina; Tecmer, Paweł; Limacher, Peter A.
  • The Journal of Chemical Physics, Vol. 140, Issue 21
  • DOI: 10.1063/1.4880820

Properties of coupled-cluster equations originating in excitation sub-algebras
journal, March 2018

  • Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 148, Issue 9
  • DOI: 10.1063/1.5010693

Adaptive Configuration Interaction for Computing Challenging Electronic Excited States with Tunable Accuracy
journal, October 2017

  • Schriber, Jeffrey B.; Evangelista, Francesco A.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 11
  • DOI: 10.1021/acs.jctc.7b00725

Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory
journal, April 1996

  • Sánchez-Marín, José; Nebot-Gil, Ignacio; Malrieu, Jean Paul
  • Theoretica Chimica Acta, Vol. 95, Issue 5-6
  • DOI: 10.1007/bf02335465

Coupled-cluster method for multideterminantal reference states
journal, October 1981


Short-range correlations in nuclear wave functions
journal, June 1960


Spin-restricted Brueckner orbitals for coupled-cluster wavefunctions
journal, December 1997

  • Crawford, T. Daniel; Lee, Timothy J.; Handy, Nicholas C.
  • The Journal of Chemical Physics, Vol. 107, Issue 23
  • DOI: 10.1063/1.475302

Coupled-cluster method tailored by configuration interaction
journal, August 2005

  • Kinoshita, Tomoko; Hino, Osamu; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 123, Issue 7
  • DOI: 10.1063/1.2000251

Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids
journal, February 2017

  • McClain, James; Sun, Qiming; Chan, Garnet Kin-Lic
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 3
  • DOI: 10.1021/acs.jctc.7b00049

A new implementation of the full CCSDT model for molecular electronic structure
journal, November 1988


Progress towards practical quantum variational algorithms
journal, October 2015


Ab-Initio Coupled-Cluster Study of O 16
journal, June 2005


Benchmark studies of variational, unitary and extended coupled cluster methods
journal, December 2010

  • Cooper, Bridgette; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 133, Issue 23
  • DOI: 10.1063/1.3520564

Relaxed active space: Fixing tailored-CC with high order coupled cluster. II
journal, February 2014

  • Melnichuk, Ann; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 140, Issue 6
  • DOI: 10.1063/1.4862676

Efficient Bayesian Phase Estimation
journal, June 2016


Coupled-cluster method in Fock space. I. General formalism
journal, August 1985


Convergence behavior of multireference perturbation theory: Forced degeneracy and optimization partitioning applied to the beryllium atom
journal, July 1996

  • Finley, James P.; Chaudhuri, Rajat K.; Freed, Karl F.
  • Physical Review A, Vol. 54, Issue 1
  • DOI: 10.1103/physreva.54.343

Partitioning technique, perturbation theory, and rational approximations: PARTITIONING TECHNIQUE
journal, January 1982

  • Löwdin, Per-Olov
  • International Journal of Quantum Chemistry, Vol. 21, Issue 1
  • DOI: 10.1002/qua.560210105

Seniority zero pair coupled cluster doubles theory
journal, June 2014

  • Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 140, Issue 21
  • DOI: 10.1063/1.4880819

A state-specific multi-reference coupled cluster formalism with molecular applications
journal, May 1998


The theory of variational hybrid quantum-classical algorithms
journal, February 2016


Analytic energy gradients for multiconfigurational self-consistent field second-order quasidegenerate perturbation theory (MC-QDPT)
journal, April 1998

  • Nakano, Haruyuki; Hirao, Kimihiko; Gordon, Mark S.
  • The Journal of Chemical Physics, Vol. 108, Issue 14
  • DOI: 10.1063/1.475975

Localized Atomic and Molecular Orbitals
journal, July 1963


Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer
journal, April 2018

  • Setia, Kanav; Whitfield, James D.
  • The Journal of Chemical Physics, Vol. 148, Issue 16
  • DOI: 10.1063/1.5019371

A new method for excited states: Similarity transformed equation-of-motion coupled-cluster theory
journal, April 1997

  • Nooijen, Marcel; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 106, Issue 15
  • DOI: 10.1063/1.474000

Brueckner's Theory and the Method of Superposition of Configurations
journal, March 1958


Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions
journal, November 2017


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

  • Cleland, Deidre; Booth, George H.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 132, Issue 4
  • DOI: 10.1063/1.3302277

A unitary multiconfigurational coupled‐cluster method: Theory and applications
journal, January 1988

  • Hoffmann, Mark R.; Simons, Jack
  • The Journal of Chemical Physics, Vol. 88, Issue 2
  • DOI: 10.1063/1.454125

Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
journal, October 2018


The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach
journal, November 2000

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 113, Issue 19
  • DOI: 10.1063/1.1318757

A method of embedding
journal, September 1981


Exponential Operators and Parameter Differentiation in Quantum Physics
journal, April 1967

  • Wilcox, R. M.
  • Journal of Mathematical Physics, Vol. 8, Issue 4
  • DOI: 10.1063/1.1705306

Improved techniques for preparing eigenstates of fermionic Hamiltonians
journal, May 2018

  • Berry, Dominic W.; Kieferová, Mária; Scherer, Artur
  • npj Quantum Information, Vol. 4, Issue 1
  • DOI: 10.1038/s41534-018-0071-5

Application of Hilbert-space coupled-cluster theory to simple ( H 2 ) 2 model systems. II. Nonplanar models
journal, May 1994


Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
journal, February 1989


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

  • Booth, George H.; Grüneis, Andreas; Kresse, Georg
  • Nature, Vol. 493, Issue 7432
  • DOI: 10.1038/nature11770

A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism
journal, August 1993

  • Piecuch, Piotr; Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 99, Issue 3
  • DOI: 10.1063/1.466179

Relaxed active space: Fixing tailored-CC with high order coupled cluster. I
journal, December 2012

  • Melnichuk, Anna; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 137, Issue 21
  • DOI: 10.1063/1.4767900

Fock-space coupled-cluster method in the intermediate Hamiltonian formulation: Model with singles and doubles
journal, June 1998

  • Meissner, Leszek
  • The Journal of Chemical Physics, Vol. 108, Issue 22
  • DOI: 10.1063/1.476377

Large basis set calculations using Brueckner theory
journal, January 1994

  • Kobayashi, Rika; Amos, Roger D.; Handy, Nicholas C.
  • The Journal of Chemical Physics, Vol. 100, Issue 2
  • DOI: 10.1063/1.466615

The full CCSDT model for molecular electronic structure
journal, June 1987

  • Noga, Jozef; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 86, Issue 12
  • DOI: 10.1063/1.452353

On the Relationship Between Continuous- and Discrete-Time Quantum Walk
journal, October 2009


Size extensivity of a general-model-space state-universal coupled-cluster method
journal, January 2004

  • Li, Xiangzhu; Paldus, Josef
  • International Journal of Quantum Chemistry, Vol. 99, Issue 6
  • DOI: 10.1002/qua.20144

Coupled-cluster method with optimized reference state
journal, March 1984

  • Stolarczyk, Leszek Z.; Monkhorst, Hendrik J.
  • International Journal of Quantum Chemistry, Vol. 26, Issue S18
  • DOI: 10.1002/qua.560260827

Erratum: The full CCSDT model for molecular electronic structure [J. Chem. Phys. 8 6 , 7041 (1987)]
journal, September 1988

  • Noga, J.; Bartlett, R. J.
  • The Journal of Chemical Physics, Vol. 89, Issue 5
  • DOI: 10.1063/1.455742

New perspectives on unitary coupled-cluster theory
journal, January 2006

  • Taube, Andrew G.; Bartlett, Rodney J.
  • International Journal of Quantum Chemistry, Vol. 106, Issue 15
  • DOI: 10.1002/qua.21198

Uncertainty relations and reduced density matrices: Mapping many-body quantum mechanics onto four particles
journal, March 2001


Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone
journal, March 2006

  • Hino, Osamu; Kinoshita, Tomoko; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 124, Issue 11
  • DOI: 10.1063/1.2180775

Structure of Fermionic Density Matrices: Complete N -Representability Conditions
journal, June 2012


The Bravyi-Kitaev transformation for quantum computation of electronic structure
journal, December 2012

  • Seeley, Jacob T.; Richard, Martin J.; Love, Peter J.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4768229

Quantum Algorithm for Spectral Measurement with a Lower Gate Count
journal, July 2018


On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces
journal, July 1987


Highly accurate treatment of electron correlation in polymers: coupled-cluster and many-body perturbation theories
journal, September 2001


Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of H : Intruder states avoidance and convergence enhancement
journal, September 1995

  • Finley, James P.; Chaudhuri, Rajat K.; Freed, Karl F.
  • The Journal of Chemical Physics, Vol. 103, Issue 12
  • DOI: 10.1063/1.470586

A variational eigenvalue solver on a photonic quantum processor
journal, July 2014

  • Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5213

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Seniority-based coupled cluster theory
journal, December 2014

  • Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar
  • The Journal of Chemical Physics, Vol. 141, Issue 24
  • DOI: 10.1063/1.4904384

Extension of coupled-cluster theory with a noniterative treatment of connected triply excited clusters to three-body Hamiltonians
journal, November 2013


The implementation of the multireference coupled‐cluster method based on the single‐reference formalism
journal, March 1992

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 96, Issue 5
  • DOI: 10.1063/1.461878

Coupled-cluster singles and doubles for extended systems
journal, February 2004

  • Hirata, So; Podeszwa, Rafał; Tobita, Motoi
  • The Journal of Chemical Physics, Vol. 120, Issue 6
  • DOI: 10.1063/1.1637577

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

Introduction of n -electron valence states for multireference perturbation theory
journal, June 2001

  • Angeli, C.; Cimiraglia, R.; Evangelisti, S.
  • The Journal of Chemical Physics, Vol. 114, Issue 23
  • DOI: 10.1063/1.1361246

Low-Depth Quantum Simulation of Materials
journal, March 2018


Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations
journal, September 2016

  • Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 145, Issue 11
  • DOI: 10.1063/1.4963082

On the solution of coupled-cluster equations in the fully correlated limit of cyclic polyene model
journal, January 1991

  • Piecuch, Piotr; Paldus, Josef
  • International Journal of Quantum Chemistry, Vol. 40, Issue S25
  • DOI: 10.1002/qua.560400807

Medium-Mass Nuclei from Chiral Nucleon-Nucleon Interactions
journal, August 2008


Analytic connection between configuration–interaction and coupled‐cluster solutions
journal, May 1978

  • Živković, Tomislav P.; Monkhorst, Hendrik J.
  • Journal of Mathematical Physics, Vol. 19, Issue 5
  • DOI: 10.1063/1.523761

Renormalization-group approach to interacting fermions
journal, January 1994


The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011


Multireference Møller—Plesset perturbation theory for high-spin open-shell systems
journal, August 1992


Use of a unitary wavefunction in the calculation of static electronic properties
journal, January 1984


NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

  • Valiev, M.; Bylaska, E. J.; Govind, N.
  • Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489
  • DOI: 10.1016/j.cpc.2010.04.018

Nuclear Saturation and Two-Body Forces: Self-Consistent Solutions and the Effects of the Exclusion Principle
journal, August 1956


Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
journal, October 2018

  • Romero, Jonathan; Babbush, Ryan; McClean, Jarrod R.
  • Quantum Science and Technology, Vol. 4, Issue 1
  • DOI: 10.1088/2058-9565/aad3e4

Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better
journal, June 2011

  • Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 134, Issue 22
  • DOI: 10.1063/1.3598471

Effective and intermediate Hamiltonians obtained by similarity transformations
journal, June 1995

  • Meissner, Leszek; Nooijen, Marcel
  • The Journal of Chemical Physics, Vol. 102, Issue 24
  • DOI: 10.1063/1.468777

Density matrix formulation for quantum renormalization groups
journal, November 1992


Multireference perturbation theory with optimized partitioning. I. Theoretical and computational aspects
journal, May 2003

  • Witek, Henryk A.; Nakano, Haruyuki; Hirao, Kimihiko
  • The Journal of Chemical Physics, Vol. 118, Issue 18
  • DOI: 10.1063/1.1563618

Optimal Hamiltonian Simulation by Quantum Signal Processing
journal, January 2017


Coupled-cluster theory in quantum chemistry
journal, February 2007


Relativistic unitary coupled cluster theory and applications
journal, March 2008

  • Sur, Chiranjib; Chaudhuri, Rajat K.; Sahoo, Bijaya K.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, Issue 6
  • DOI: 10.1088/0953-4075/41/6/065001

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

  • Booth, George H.; Thom, Alex J. W.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 131, Issue 5
  • DOI: 10.1063/1.3193710

Multireference coupled‐cluster method using a single‐reference formalism
journal, January 1991

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 94, Issue 2
  • DOI: 10.1063/1.460031

Correlation problem in open-shell atoms and molecules: A non-perturbative linked cluster formulation
journal, December 1975

  • Mukherjee, Debashis; Moitra, Raj Kumar; Mukhopadhyay, Atri
  • Molecular Physics, Vol. 30, Issue 6
  • DOI: 10.1080/00268977500103351

Bound states of a many-particle system
journal, June 1958


Optimum phase-shift estimation and the quantum description of the phase difference
journal, November 1996


A note on the Zassenhaus product formula
journal, March 2006

  • Scholz, Daniel; Weyrauch, Michael
  • Journal of Mathematical Physics, Vol. 47, Issue 3
  • DOI: 10.1063/1.2178586

Fermionic Quantum Computation
journal, May 2002


Computing coupled-cluster wave functions with arbitrary excitations
journal, July 2000

  • Kállay, Mihály; Surján, Péter R.
  • The Journal of Chemical Physics, Vol. 113, Issue 4
  • DOI: 10.1063/1.481925

On the difference between variational and unitary coupled cluster theories
journal, January 2018

  • Harsha, Gaurav; Shiozaki, Toru; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 148, Issue 4
  • DOI: 10.1063/1.5011033

Intruder state avoidance multireference Møller-Plesset perturbation theory: Multireference Møller-Plesset Perturbation Theory
journal, May 2002

  • Witek, Henryk A.; Choe, Yoong-Kee; Finley, James P.
  • Journal of Computational Chemistry, Vol. 23, Issue 10
  • DOI: 10.1002/jcc.10098

Robust calibration of a universal single-qubit gate set via robust phase estimation
journal, December 2015


Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm
journal, February 2018


N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant
journal, December 2001


A general model‐space coupled‐cluster method using a Hilbert‐space approach
journal, January 1990

  • Meissner, Leszek; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 92, Issue 1
  • DOI: 10.1063/1.458406

Coupled‐cluster method truncated at quadruples
journal, November 1991

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 95, Issue 9
  • DOI: 10.1063/1.461534

A fast intrinsic localization procedure applicable for a b i n i t i o and semiempirical linear combination of atomic orbital wave functions
journal, May 1989

  • Pipek, János; Mezey, Paul G.
  • The Journal of Chemical Physics, Vol. 90, Issue 9
  • DOI: 10.1063/1.456588

Optimizing the density-matrix renormalization group method using quantum information entropy
journal, November 2003


Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory
journal, November 1984


Quantum algorithms revisited
journal, January 1998

  • Cleve, R.; Ekert, A.; Macchiavello, C.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969
  • DOI: 10.1098/rspa.1998.0164

Many‐body similarity transformations generated by normal ordered exponential excitation operators
journal, February 1996

  • Nooijen, Marcel
  • The Journal of Chemical Physics, Vol. 104, Issue 7
  • DOI: 10.1063/1.470988

Coupled Cluster Calculations of Ground and Excited States of Nuclei
journal, April 2004


Brueckner based generalized coupled cluster theory: Implicit inclusion of higher excitation effects
journal, September 2000

  • Nooijen, Marcel; Lotrich, Victor
  • The Journal of Chemical Physics, Vol. 113, Issue 11
  • DOI: 10.1063/1.1288912

Comparison of low-order multireference many-body perturbation theories
journal, April 2005

  • Chaudhuri, Rajat K.; Freed, Karl F.; Hose, Gabriel
  • The Journal of Chemical Physics, Vol. 122, Issue 13
  • DOI: 10.1063/1.1863912

Error mitigation extends the computational reach of a noisy quantum processor
journal, March 2019


Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation
journal, February 2015


A state-specific multi-reference coupled cluster formalism with molecular applications
journal, May 1998