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.

5 pages, 5 figures, accepted for publication in Phys. Rev. A

References in corpus (6)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Quantum Algorithms for Fermionic Simulations
• Optimal Quantum Measurements of Expectation Values of Observables
• Quantum Simulations on a Quantum Computer
• Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator

Cited by in corpus (7)

• Simulating chemistry using quantum computers
• Using Quantum Computers for Quantum Simulation
• Adiabatic state preparation study of methylene
• Introduction to Quantum Algorithms for Physics and Chemistry
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Quantum algorithms for powering stable Hermitian matrices