Adiabatic oracle for Grover's algorithm*

Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle, which is a specific unitary operation. Generation of this oracle is formally beyond the original algorithm design. Here, we propose a realization of Grover's oracle for a large class of searching problems using a quantum annealing step. The time of this step grows only logarithmically with the size of the database. This suggests an efficient path to application of Grover's algorithm to practically important problems, such as finding the ground state of a Hamiltonian with a spectral gap over its ground state.