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

TL;DR

This paper introduces a quantum computing method that uses the evolution of a physical quantity's mean value to determine energy levels, enabling efficient analysis of complex quantum systems like the Ising model.

Contribution

It proposes a novel approach for estimating energy levels on quantum computers by analyzing the time evolution of specific physical quantities, advancing quantum simulation capabilities.

Findings

Method successfully applied to spin systems and Ising models

Demonstrated on IBM quantum computers with promising results

Potential to achieve quantum supremacy in energy estimation

Abstract

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.