  This paper presents a deterministic search algorithm on complete bipartite
graphs. Our algorithm adopts the simple form of alternating iterations of an
oracle and a continuous-time quantum walk operator, which is a generalization
of Grover's search algorithm. We address the most general case of multiple
marked states, so there is a problem of estimating the number of marked states.
To this end, we construct a quantum counting algorithm based on the spectrum
structure of the search operator. To implement the continuous-time quantum walk
operator, we perform Hamiltonian simulation in the quantum circuit model. We
achieve simulation in constant time, that is, the complexity of the quantum
circuit does not scale with the evolution time.
