We show how to leverage quantum annealers to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use quantum annealers that sample from the ground state(s) of a problem-dependent Ising Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results, on a D-Wave 2000Q quantum processor, revealed that the proposed quantum-assisted greedy algorithm (QAGA) can find notably better solutions (i.e., samples with lower energy value), compared to the state-of-the-art techniques in the realm of quantum annealing.