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In this paper we outline the extension of recently introduced the sub-systemembedding sub-algebras coupled cluster (SES-CC) formalism to the unitary CCformalism. In analogy to the standard single-reference SES-CC formalism, itsunitary CC extension allows one to include the dynamical (outside the activespace) correlation effects in an SES induced complete active space (CAS)effective Hamiltonian. In contrast to the standard single-reference SES-CCtheory, the unitary CC approach results in a Hermitian form of the effectiveHamiltonian. Additionally, for the double unitary CC formalis (DUCC) thecorresponding CAS eigenvalue problem provides a rigorous separation of externalcluster amplitudes that describe dynamical correlation effects - used to definethe effective Hamiltonian - from those corresponding to the internal (insidethe active space) excitations that define the components of eigenvectorsassociated with the energy of the entire system. The proposed formalism can beviewed as an efficient way of downfolding many-electron Hamiltonian to thelow-energy model represented by a particular choice of CAS. In principle, thistechnique can be extended to any type of complete active space representing anarbitrary energy window of a quantum system. The Hermitian character oflow-dimensional effective Hamiltonians makes them an ideal target for severaltypes of full configuration interaction (FCI) type eigensolvers. As an example,we also discuss the algebraic form of the perturbative expansions of theeffective DUCC Hamiltonians corresponding to composite unitary CC theories anddiscuss possible algorithms for hybrid classical and quantum computing.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

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