The quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving NPcomplete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one in the evolution. In this paper we show a way of speedup in the quantum adiabatic evolution algorithm, using an extended Hamiltonian. We present the exact relation between the energy gap and the elements of the extended Hamiltonian, which provides a new point of view to reduce the running time.
A Journal of Physical Sciences: Zeitschrift für Naturforschung A (ZNA) is an international scientific journal which publishes original research papers from all areas of experimental and theoretical physics. In accordance with the name of the journal, which means “Journal for Natural Sciences”, manuscripts submitted to ZNA should have a tangible connection to actual physical phenomena.