  The negative hydrogen ion is the first three body quantum problem whose
ground state energy is calculated using the `Chandrasekhar Wavefunction' that
accounts for the electron-electron correlation. Solving multi-body systems is a
daunting task in quantum mechanics as it includes choosing a trial wavefunction
and the calculation of integrals for the system that becomes almost impossible
for systems with three or more particles. This difficulty can be addressed by
quantum computers. They have emerged as a tool to address different electronic
structure problems with remarkable efficiency. They have been realized in
various fields and proved their efficiency over classical computers. Here, we
show the quantum simulation of H^{-} ion to calculate it's ground state energy
in IBM quantum computer. The energy is found to be -0.5339355468 Hartree with
an error of 0.8376% as compared to the theoretical value. We observe that the
quantum computer is efficient in preparing the correlated wavefunction of H^{-}
and calculating it's ground state energy. We use a recently developed algorithm
known as `Variational Quantum Eigensolver' and implement it in IBM's 5-qubit
quantum chip `ibmqx2'. The method consists of a quantum part i.e., state
preparation and measurement of expectation values using the quantum computer,
and the classical part i.e., the optimization routine run in a classical
computer for energy convergence. An optimization routine is performed on
classical computer by running quantum chemistry program and codes in QISKit to
converge the energy to the minimum. We also present a comparison of different
optimization routines and encoding methods used to converge the energy value to
the minimum. The technique can be used to solve various many body problems with
great efficiency.
