  Quantum chemistry has been viewed as one of the potential early applications
of quantum computing. Two techniques have been proposed for electronic
structure calculations: (i) the variational quantum eigensolver and (ii) the
phase-estimation algorithm. In both cases, the complexity of the problem
increases for basis sets where either the Hamiltonian is not sparse, or it is
sparse, but many orbitals are required to accurately describe the molecule of
interest. In this work, we explore the possibility of mapping the molecular
problem onto a sparse Hubbard-like Hamiltonian, which allows a
Green's-function-based approach to electronic structure via a hybrid
quantum-classical algorithm. We illustrate the time-evolution aspect of this
methodology with a simple four-site hydrogen ring.
