  We propose a circuit-model quantum algorithm for eigenpath traversal that is
based on a combination of concepts from Grover's search and adiabatic quantum
computation. Our algorithm deploys a sequence of reflections determined from
eigenspaces of instantaneous Hamiltonians defined along an adiabatic schedule
in order to prepare a ground state of a target problem Hamiltonian. We provide
numerical evidence suggesting that, for combinatorial search problems, our
algorithm can find a solution faster, on average, than Grover's search. We
demonstrate our findings by applying both algorithms to solving the NP-hard
MAX-2SAT problem.
