Quantum computational method of finding the ground-state energy and expectation values

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We propose a 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 noninteracting 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 the 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.

Original languageEnglish
Article number012326
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume77
Issue number1
DOIs
Publication statusPublished - 22 Jan 2008
Externally publishedYes

Fingerprint

ground state
energy
Hellmann-Feynman theorem
harmonic oscillators
oscillators
scattering

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

Cite this

@article{e932786b7a1b4987ab34e37c8c4cdc18,
title = "Quantum computational method of finding the ground-state energy and expectation values",
abstract = "We propose a 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 noninteracting 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 the 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.",
author = "Sangchul Oh",
year = "2008",
month = "1",
day = "22",
doi = "10.1103/PhysRevA.77.012326",
language = "English",
volume = "77",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Quantum computational method of finding the ground-state energy and expectation values

AU - Oh, Sangchul

PY - 2008/1/22

Y1 - 2008/1/22

N2 - We propose a 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 noninteracting 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 the 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.

AB - We propose a 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 noninteracting 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 the 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.

UR - http://www.scopus.com/inward/record.url?scp=38549181286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38549181286&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.77.012326

DO - 10.1103/PhysRevA.77.012326

M3 - Article

AN - SCOPUS:38549181286

VL - 77

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 1

M1 - 012326

ER -