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

TL;DR

This paper introduces a quantum computational method combining adiabatic evolution and phase estimation to accurately find ground state energies and expectation values of interacting Hamiltonians, demonstrated on several models.

Contribution

It presents a novel quantum approach integrating adiabatic evolution and phase estimation for ground state calculations, improving accuracy for complex systems.

Findings

Results agree well with known solutions

Effective for anharmonic and scattering models

Demonstrates potential for quantum simulation of many-body systems

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.