  Quantum chemistry is regarded to be one of the first disciplines that will be
revolutionized by quantum computing. Although universal quantum computers of
practical scale may be years away, various approaches are currently being
pursued to solve quantum chemistry problems on near-term gate-based quantum
computers and quantum annealers by developing the appropriate algorithm and
software base. This work implements the general Quantum Annealer Eigensolver
(QAE) algorithm to solve the molecular electronic Hamiltonian
eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach
is based on the matrix formulation, efficiently uses qubit resources based on a
power-of-two encoding scheme and is hardware-dominant relying on only one
classically optimized parameter. We demonstrate the use of D-Wave hardware for
obtaining ground and electronically excited states across a variety of small
molecular systems. This approach can be adapted for use by a vast majority of
electronic structure methods currently implemented in conventional
quantum-chemical packages. The results of this work will encourage further
development of software such as qbsolv which has promising applications in
emerging quantum information processing hardware and is able to address large
and complex optimization problems intractable for classical computers.
