Energy levels estimation on a quantum computer by evolution of a
  physical quantity
We show that the time dependence of mean value of a physical quantity is
related with the transition energies of a quantum system. In the case when the
operator of a physical quantity anticommutes with the Hamiltonian of a system,
studies of the evolution of its mean value allow determining the energy levels
of the system. On the basis of the result, we propose a method for determining
energy levels of physical systems on a quantum computer. The method opens a
possibility to achieve quantum supremacy in solving the problem of finding
minimal or maximal energy of Ising model with spatially anisotropic interaction
using multi-qubit quantum computers. We apply the method for spin systems (spin
in magnetic field, spin chain, Ising model on squared lattice) and realize it
on IBM's quantum computers.
Kh. P. Gnatenko H. P. Laba V. M. Tkachuk