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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]
+ Show Author Affiliations
  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 Laboratory (PNNL), Richland, WA (United States); Quantum Information Science (QIS)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and 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.
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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. https://doi.org/10.1063/1.5094643
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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. https://doi.org/10.1063/1.5094643. https://www.osti.gov/servlets/purl/1574813.
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@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}
}
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FIG. 1 FIG. 1: Abstract representation of the SES-CC approach.
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  • 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

Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory
journal, January 1997

  • Sánchez-Marín, José; Nebot-Gil, Ignacio; Malrieu, Jean Paul
  • Theoretica Chimica Acta, Vol. 95, Issue 5
  • DOI: 10.1007/s002140050193

Seniority-based coupled cluster theory
text, January 2014

Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
text, January 2014

Optimal Hamiltonian Simulation by Quantum Signal Processing
text, January 2016

Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
text, January 2017

The density-matrix renormalization group
text, January 2004

A note on the Zassenhaus product formula
text, January 2006

Coupled cluster calculations of ground and excited states of nuclei
text, January 2003

Relativistic unitary coupled cluster theory and applications
preprint, January 2005

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    Quantum simulations of excited states with active-space downfolded Hamiltonians
    journal, December 2019

    • Bauman, Nicholas P.; Low, Guang Hao; Kowalski, Karol
    • The Journal of Chemical Physics, Vol. 151, Issue 23
    • DOI: 10.1063/1.5128103
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