Energy levels estimation on a quantum computer by evolution of a physical quantity

•Method for detecting energy levels of physical systems on quantum computer is proposed.•The method is based on the studies of evolution of mean value of physical quantity.•Energy levels of spin systems are detected on IBM's quantum computer. We show that the time dependence of mean value of a physical quantity is related with the transition energies of a quantum system. We also find that studies of evolution of mean value of operator anticommuting with Hamiltonian of a system allow to detect directly its energy levels. On the basis of the obtained results, we propose a method for detecting energy levels of physical systems on a quantum computer by evolution of a physical quantity. 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 finding energy levels of spin systems (spin in magnetic field, spin chain, Ising model on squared lattice) and realize it on IBM's quantum computers.