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 »
- Authors:
-
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States). William R. Wiley Environmental Molecular Sciences Lab.
- 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.
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
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.
@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}
}
Web of Science
Figures / Tables:

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Works referencing / citing this record:
Quantum simulations of excited states with active-space downfolded Hamiltonians
journal, December 2019
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- The Journal of Chemical Physics, Vol. 151, Issue 23
Compact Molecular Simulation on Quantum Computers via Combinatorial Mapping and Variational State Preparation
preprint, January 2022
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- arXiv
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