QAOA-Predictor: Forecasting Success Probabilities and Minimal Depths for Efficient Fixed-Parameter Optimization

TL;DR

This paper introduces a Graph Neural Network-based method to predict the success probabilities and minimal layer depths for QAOA, enabling efficient fixed-parameter optimization without extensive parameter tuning.

Contribution

The study presents a novel GNN approach to forecast QAOA performance, generalizing across problem types and sizes, reducing the need for costly optimization.

Findings

GNN predicts QAOA success probabilities within 10% accuracy.

Model generalizes to unseen problem classes and larger sizes.

Enables selection of problem instances and optimal parameters without extensive tuning.

Abstract

Quantum Computing promises to solve complex combinatorial optimization problems more efficiently than classical methods, with the Quantum Approximate Optimization Algorithm (QAOA) being a leading candidate. Recent fixed-parameter variations of QAOA eliminate costly run-time optimization, but determining their optimal initialization as well as the number of required layers (p) for a target solution remains a critical, unsolved challenge. In this work, we propose a novel approach using a Graph Neural Network (GNN) to predict QAOA performance: Based on a graph representation of the problem, the GNN forecasts the probability of the optimal solution in the resulting distribution across different parameter initializations and layer depths for a wide variety of combinatorial optimization problems. We demonstrate that the GNN accurately predicts QAOA performance within a 10% margin of the true values. Furthermore, the model exhibits strong generalization capabilities across unseen problem classes, larger problem sizes, and higher layer counts. Our approach allows to identify viable problem instances for QAOA and to select an adequate parameter initialization strategy with minimal layer depth, without the need of costly parameter optimization.