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

Bauman, Nicholas P.; Bylaska, Eric J.; Krishnamoorthy, Sriram; Low, Guang Hao; Wiebe, Nathan; Granade, Christopher E.; Roetteler, Martin; Troyer, Matthias; Kowalski, Karol

doi:10.1063/1.5094643

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

Journal Article · Wed Jul 03 00:00:00 EDT 2019 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5094643· OSTI ID:1574813

^[1];

^[1]; Krishnamoorthy, Sriram ^[1]; Low, Guang Hao ^[2]; Wiebe, Nathan ^[2]; Granade, Christopher E. ^[2];

^[2];

^[1]

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

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.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Quantum Information Science (QIS)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1574813

Alternate ID(s):: OSTI ID: 1530913; OSTI ID: 1598634

Report Number(s):: PNNL-SA-141041; TRN: US2001250

Journal Information:: Journal of Chemical Physics, Vol. 151, Issue 1; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 36 works

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Quantum simulations of excited states with active-space downfolded Hamiltonians Bauman, Nicholas P.; Low, Guang Hao; Kowalski, Karol The Journal of Chemical Physics, Vol. 151, Issue 23 https://doi.org/10.1063/1.5128103	journal	December 2019
Compact Molecular Simulation on Quantum Computers via Combinatorial Mapping and Variational State Preparation Chamaki, Diana; Metcalf, Mekena; de Jong, Wibe A. arXiv https://doi.org/10.48550/arxiv.2205.11742	preprint	January 2022

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Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Quantum Information Science (QIS)
ab initio
coupled-cluster
quantum chemistry
quantum computing