  Local quantum annealing (LQA), an iterative algorithm, is designed to solve
combinatorial optimization problems. It draws inspiration from QA, which
utilizes adiabatic time evolution to determine the global minimum of a given
objective function. In the original LQA, the classical Hamiltonian is minimized
via gradient descent. The performance of LQA depends on the choice of the
parameters. Owing to the non-convex nature of the original cost function, LQA
often becomes trapped in local minima, limiting its effectiveness. To address
this challenge, we combine LQA with a deep unfolding scheme, which enables us
to tune the parameters from the training data via back-propagation. Our
findings demonstrate that deep unfolded LQA outperforms the original LQA,
exhibiting remarkable convergence speed and performance improvement. As the
trained parameters can be generalized to unknown instances and different system
sizes, our results have significant practical implications and provide valuable
insights for real-world applications.
