  Variational quantum algorithms are emerging as promising candidates for
near-term practical applications of quantum information processors, in the
field of quantum chemistry. We implement the variational quantum eigensolver
algorithm to calculate the molecular ground-state energy of the H2 molecule and
experimentally demonstrated it on an NMR quantum processor. Further, we
simulate the excited states of the H2 molecule using the variational quantum
deflation algorithm and experimentally demonstrate it on the same NMR quantum
processor. We also develop the first simulation of the energy calculation of
the H2 molecule using only a single qubit, and verify the results on an NMR
quantum computer. Our experimental results demonstrate that only a single NMR
qubit suffices to calculate the molecular energies of the H2 molecule to the
desired accuracy.
