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Adiabatic quantum computation, based on the adiabatic theorem, is a promisingalternative to conventional quantum computation. The validity of an adiabaticalgorithm depends on the existence of a nonzero energy gap between the groundand excited states. However, it is difficult to ascertain the exact value ofthe energy gap. In this paper, we put forward a theorem on the existence ofnonzero energy gap for the Hamiltonians used in adiabatic quantum computation.It can help to effectively identify a large class of the Hamiltonians withoutenergy-level crossing between the ground and excited states.

Theorem on the existence of a nonzero energy gap in adiabatic quantum computation