An adiabatic quantum algorithm and its application to DNA motif model discovery

In this paper, we deal with the adiabatic approximation of general Hamiltonians by splitting it into two parts, with one part a Hamiltonian that has at least one time-independent eigenstate up to a phase factor. We first develop the method of finding this kind of Hamiltonians. Then the relationship between adiabatic approximation and these Hamiltonians is discussed. Applying this to a general case, we give both a necessary condition and a sufficient condition for adiabatic approximation, followed by a spin-half example to illustrate.

Analysis of Adiabatic Approximation Using Stable Hamiltonian Method

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Analysis of Adiabatic Approximation Using Stable Hamiltonian Method