  Quantum computing is a computational paradigm with the potential to
outperform classical methods for a variety of problems. Proposed recently, the
Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the
leading candidates for demonstrating quantum advantage in the near term. QAOA
is a variational hybrid quantum-classical algorithm for approximately solving
combinatorial optimization problems. The quality of the solution obtained by
QAOA for a given problem instance depends on the performance of the classical
optimizer used to optimize the variational parameters. In this paper, we
formulate the problem of finding optimal QAOA parameters as a learning task in
which the knowledge gained from solving training instances can be leveraged to
find high-quality solutions for unseen test instances. To this end, we develop
two machine-learning-based approaches. Our first approach adopts a
reinforcement learning (RL) framework to learn a policy network to optimize
QAOA circuits. Our second approach adopts a kernel density estimation (KDE)
technique to learn a generative model of optimal QAOA parameters. In both
approaches, the training procedure is performed on small-sized problem
instances that can be simulated on a classical computer; yet the learned RL
policy and the generative model can be used to efficiently solve larger
problems. Extensive simulations using the IBM Qiskit Aer quantum circuit
simulator demonstrate that our proposed RL- and KDE-based approaches reduce the
optimality gap by factors up to 30.15 when compared with other commonly used
off-the-shelf optimizers.
