Equivariant Quantum Graph Neural Network for Mixed-Integer Linear Programming
Primary Area: learning on graphs and other geometries & topologies
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Keywords: Quantum machine learning, Quantum graph circuit, Mixed-integer linear programming
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Abstract: Mixted-integer linear programming (MILP) is an essential task for operation research, especially for combinatorial optimization problems. Apart from the classic non-learning solvers that often resort to heuristics, recent machine learning-based models have been actively studied, and graph neural networks (GNNs) have been dominantly adopted. However, recent literature has shown that the GNNs based on message passing mechanism suffer fundamental expressiveness limitations in MILP instance representation, in the sense that two different MILP instances could be eventually embedded into exactly the same feature. In this paper, we resort to the quantum mechanism and develop a tailored quantum counterpart of GNNs, called equivariant quantum GNN (EQGNN), which can guarantee to distinguish any two MILPs, i.e., leading to different graph embeddings. EQGNN designs a novel quantum parametric circuit that can encode node and edge features while maintaining the property of permutation equivariance. To enhance the expressivity power of the model, we also introduce an auxiliary layer with an optional number of auxiliary qubits. Experimental results demonstrate the effectiveness of the method in solving MILP problems and the trainability of the model with increasing system scale. Compared with GNN, EQGNN can achieve better separation power and generalization performance with fewer parameters.
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Submission Number: 5720
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