Abstract: The adiabatic theorem in quantum mechanics enables us to derive new algorithms in quantum computation (QC) and gives us a new perspective on QC itself. Using the adiabatic theorem we are able to find ground eigenstates of a potentially complicated Hamiltonian $H_1$ by constructing a time dependent Hamiltonian $H(t)$. If $H_0=H(0)$ is suitably chosen, its eigenstates may be constructed easily; the adiabatic evolution then uncovers the eigenstates of the examined Hamiltonian $H_1$.
We introduce the basic concepts of adiabatic quantum computation (AQC), examine Grover's problem and show the relation between AQC and the adiabatic theorem in quantum mechanics. We will also relate AQC to the standard circuit model.