Detecting Energy Levels of Spin Systems on IBM’s Quantum Computer by Evolution of Mean Value of Physical Quantity

Finding energy levels of a quantum system is an important problem that can be solved using quantum computers. We showed that transition energies of a quantum system are related with the evolution of mean value of a physical quantity. In particular case when the operator of a physical quantity anticommutes with the Hamiltonian of a system we found that studies of the evolution of the mean value of this physical quantity give a possibility to determine the energy levels of the system and their degeneracy. On the basis of the results the energy levels of spin systems were detected on IBMs quantum computers ibmq manila and ibmq melbourne. It is worth noting that spin systems are one of the most suitable systems for modeling them on a quantum computer. We considered a spin in magnetic field, spin chain with Ising interaction, spin square-lattice with isotropic and spatially anisotropic Ising interactions. The results obtained on the quantum devices correspond to the analytical one. It is important to note that finding the maximal or the minimal energy of the Ising model on square lattice with spatially anisotropic interaction is not a trivial problem. Therefore, the proposed algorithm for obtaining the energy levels opens a possibility to achieve the quantum supremacy in solving this problem on many qubit quantum computers.