  We introduce the idea of using adiabatic rotation to generate superpositions
of a large class of quantum states. For quantum computing this is an
interesting alternative to the well-studied "straight line" adiabatic
evolution. In ways that complement recent results, we show how to efficiently
prepare three types of states: Kitaev's toric code state, the cluster state of
the measurement-based computation model and the history state used in the
adiabatic simulation of quantum circuit. We also show that the method, when
adapted for quantum search, provides quadratic speedup as other optimal methods
do with the advantages that the problem Hamiltonian is time-independent and
that the energy gap above the ground state is strictly nondecreasing with time.
Likewise the method can be used for optimization as an alternative to the usual
adiabatic algorithm.
