  Quadratic unconstrained binary optimization (QUBO) tasks are very important
in chemistry, finance, job scheduling, and so on, which can be represented
using graph structures, with the variables as nodes and the interaction between
them as edges. Variational quantum algorithms, especially the Quantum
Approximate Optimization Algorithm (QAOA) and its variants, present a promising
way, potentially exceeding the capabilities of classical algorithms, for
addressing QUBO tasks. However, the possibility of using message-passing
machines, inspired by classical graph neural networks, to enhance the power and
performance of these quantum algorithms for QUBO tasks was not investigated.
This study introduces a novel variational quantum graph optimization algorithm
that integrates the message-passing mechanism, which demonstrates significant
improvements in performance for solving QUBO problems in terms of resource
efficiency and solution precision, compared to QAOA, its variants, and other
quantum graph neural networks. Furthermore, in terms of scalability on QUBO
tasks, our algorithm shows superior performance compared to QAOA, presenting a
substantial advancement in the field of quantum approximate optimization.
