  The Quantum Approximate Optimization Algorithm (QAOA), a pivotal paradigm in
the realm of variational quantum algorithms (VQAs), offers promising
computational advantages for tackling combinatorial optimization problems.
Well-defined initial circuit parameters, responsible for preparing a
parameterized quantum state encoding the solution, play a key role in
optimizing QAOA. However, classical optimization techniques encounter
challenges in discerning optimal parameters that align with the optimal
solution. In this work, we propose a hybrid optimization approach that
integrates Gated Recurrent Units (GRU), Convolutional Neural Networks (CNN),
and a bilinear strategy as an innovative alternative to conventional optimizers
for predicting optimal parameters of QAOA circuits. GRU serves to
stochastically initialize favorable parameters for depth-1 circuits, while CNN
predicts initial parameters for depth-2 circuits based on the optimized
parameters of depth-1 circuits. To assess the efficacy of our approach, we
conducted a comparative analysis with traditional initialization methods using
QAOA on Erd\H{o}s-R\'enyi graph instances, revealing superior optimal
approximation ratios. We employ the bilinear strategy to initialize QAOA
circuit parameters at greater depths, with reference parameters obtained from
GRU-CNN optimization. This approach allows us to forecast parameters for a
depth-12 QAOA circuit, yielding a remarkable approximation ratio of 0.998
across 10 qubits, which surpasses that of the random initialization strategy
and the PPN2 method at a depth of 10. The proposed hybrid GRU-CNN bilinear
optimization method significantly improves the effectiveness and accuracy of
parameters initialization, offering a promising iterative framework for QAOA
that elevates its performance.
