  Providing an optimal path to a quantum annealing algorithm is key to finding
good approximate solutions to computationally hard optimization problems.
Reinforcement is one of the strategies that can be used to circumvent the
exponentially small energy gaps of the system in the annealing process. Here a
time-dependent reinforcement term is added to the Hamiltonian in order to give
lower energies to the most probable states of the evolving system. In this
study, we take a local entropy in the configuration space for the reinforcement
and apply the algorithm to a number of easy and hard optimization problems. The
reinforced algorithm performs better than the standard quantum annealing
algorithm in the quantum search problem, where the optimal parameters behave
very differently depending on the number of solutions. Moreover, the
reinforcements can change the discontinuous phase transitions of the mean-field
p-spin model ($p>2$) to a continuous transition. The algorithm's performance in
the binary perceptron problem is also superior to that of the standard quantum
annealing algorithm, which already works better than a classical simulated
annealing algorithm.
