Conditional Diffusion-based Parameter Generation for Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces a diffusion-based generative model to produce effective initial parameters for QAOA, significantly enhancing its performance on MaxCut problems by leveraging dataset-conditioned parameter sampling.

Contribution

It proposes a novel dataset-conditioned diffusion model for generating initial QAOA parameters, improving optimization efficiency and solution quality over traditional random initialization methods.

Findings

Improves approximation ratio by up to 14.4% on various MaxCut instances.

Conditional DDPM trained on small instances generalizes to larger ones, boosting performance.

Demonstrates the effectiveness of diffusion models in quantum algorithm parameter initialization.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm that shows promise in efficiently solving the MaxCut problem, a representative example of combinatorial optimization. However, its effectiveness heavily depends on the parameter optimization pipeline, where the parameter initialization strategy is nontrivial due to the non-convex and complex optimization landscapes characterized by issues with low-quality local minima. Recent inspiration comes from the diffusion of classical neural network parameters, which has demonstrated that neural network training can benefit from generating good initial parameters through diffusion models. Therefore, in this work, we formulate the problem of finding good initial parameters as a generative task and propose the initial parameter generation scheme through dataset-conditioned pre-trained parameter sampling. Concretely, the generative machine learning model, specifically the denoising diffusion probabilistic model (DDPM), is trained to learn the distribution of pretrained parameters conditioned on the graph dataset. Intuitively, our proposed framework aims at effectively distilling knowledge from pre-trained parameters to generate well-performing initial parameters for QAOA. Compared to random parameter initialization, experiments on various-sized Max-Cut problem instances consistently show that our conditional DDPM is capable of improving the approximation ratio by as much as 14.4%, 11.0%, 11.4% and 7.49%, 8.31%, 6.08% on average for random, regular, and Watts-Strogatz graphs, respectively. Additionally, the experimental results also indicate that the conditional DDPM trained on small problem instances can be extrapolated to larger ones, improving the approximation ratio by up to 28.4% and 12.1% on average.