  Various methods have been developed for the quantum computation of the ground
and excited states of physical and chemical systems, but many of them require
either large numbers of ancilla qubits or high-dimensional optimization. The
quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods
proposed in [1] eschew the aforementioned issues. In this study, we demonstrate
the practical application of these algorithms to nontrivial quantum
computation, using the deuteron binding energy and molecular Hydrogen binding
and excited state energies as examples. With the correct choice of initial and
final states, we show that the number of time steps in QITE and QLanczos can be
reduced significantly, which commensurately simplifies the required quantum
circuit and improves compatibility with NISQ devices. We have performed these
calculations on cloud-accessible IBM-Q quantum computers. With the application
of readout-error mitigation and Richardson error extrapolation, we have
obtained ground and excited state energies that agree well with exact results
obtained from diagonalization.
