  Quantum computing presents a compelling prospect for revolutionizing the
field of combinatorial optimization, in virtue of the unique attributes of
quantum mechanics such as superposition and entanglement. The Quantum
Approximate Optimization Algorithm (QAOA), which is a variational hybrid
quantum-classical algorithm, stands out as leading proposals to efficiently
solve the Max-Cut problem, a representative example of combinatorial
optimization. However, its promised advantages strongly rely on parameters
initialization strategy, a critical aspect due to the non-convex and complex
optimization landscapes characterized by low-quality local minima issues.
Therefore, in this work, we formulate the problem of finding good initial
parameters as a generative task in which the generative machine learning model,
specifically the denoising diffusion probabilistic model (DDPM), is trained to
generate high-performing initial parameters for QAOA. The diffusion model is
capable of learning the distribution of high-performing parameters and then
synthesizing new parameters closer to optimal ones. Experiments with various
sized Max-Cut problem instances demonstrate that our diffusion process
consistently enhances QAOA effectiveness compared to random parameters
initialization. Moreover, our framework indicates the capacity of training on
small, classically simulatable problem instances, aiming at extrapolating to
larger instances to reduce quantum computational resource overhead.
