Quantum Computational Method of Finding the Ground State Energy and Expectation Values

Abstract

We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of a non-interacting Hamiltonian onto a ground state of an interacting Hamiltonian and the phase estimation algorithm to retrieve the ground-state energy. The expectation value of an observable for the ground state is obtained with the help of Hellmann-Feynman theorem. As an illustration of our method, we consider a displaced harmonic oscillator, a quartic anharmonic oscillator,and a potential scattering model. The results obtained by this method are in good agreement with the known results.