C2QA Quantum Thursdays - Karol Kowalski

Dimensionality reduction of many-body problem using coupled-cluster formalism: hybrid quantum-classical computing perspective

 

Join: Zoom Meeting https://bnl.zoomgov.com/j/1609999793?pwd=VWdlYlhIVGJUQTRTY0M3WFN3dzFzdz09

 

ABSTRACT: 

Novel and predictive modeling tools for overcoming exponential computational barriers in computational chemistry are needed to describe chemical transformations that involve challenging quasi-degenerate electronic states. These states are commonly encountered in modeling chemical processes related to catalysis, actinide chemistry, nitrogen fixation, and energy storage materials. To address these challenges, we have recently introduced an extension of the sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to the unitary CC (UCC) formulation, which provides a Hermitian form of the effective Hamiltonian defined in the complete active spaces (CASs). It was shown that the utilization of the so-called double unitary CC formalism (DUCC) provides a rigorous separation between external (dynamical) and internal (static) correlation effects in the active space-effective Hamiltonians. 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. The Hermitian character of low-dimensionality effective Hamiltonians makes them an ideal target for quantum computing. To illustrate the performance and feasibility of the DUCC formalism, we will provide results obtained with the Quantum Phase Estimator (QPE) and Variational Quantum Eigensolver (VQE) for benchmark molecular systems described by Gaussian and plane-wave basis sets. We will also outline recent extensions of downfolding quantum algorithms to (1) the time-domain, (2) local formulations, and (3) quantum flow equations that offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.