  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.
