Molecular docking is important in drug discovery but is burdensome for classical computers. Here, we introduce Grid Point Matching (GPM) and Feature Atom Matching (FAM) to accelerate pose sampling in molecular docking by encoding the problem into quadratic unconstrained binary optimization (QUBO) models so that it could be solved by quantum computers like the coherent Ising machine (CIM). As a result, GPM shows a sampling power close to that of Glide SP, a method performing an extensive search. Moreover, it is estimated to be 1000 times faster on the CIM than on classical computers. Our methods could boost virtual drug screening of small molecules and peptides in future.