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 · 02 July 2019 · Journal of Chemical Physics

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

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^[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

Here, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (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 (DUCC) formalism, the corresponding CAS eigenvalue problem provides a rigorous separation 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 CAS 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 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. Given growing interest in quantum computing, we provide energies for H₂ and Be systems obtained with the quantum phase estimator algorithm available in the Quantum Development Kit for the approximate DUCC Hamiltonians.

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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) (SC-22). Chemical Sciences, Geosciences & 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

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

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

Country of Publication:: United States

Language:: English

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