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

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

2007-12-05

arxiv.org/abs/0712.0789v1

Phys. Rev. A 77, 012326 (2008)

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.77.012326

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.

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