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QubitE: Qubit Embedding for Knowledge Graph Completion

Knowledge graph embeddings (KGEs) learn low-dimensional representations of entities and relations to predict missing facts based on existing ones. Quantum-based KGEs utilise variational quantum circuits for link prediction and score triples via the probability distribution of measuring the qubit states. However, there exists another best measurement for training variational quantum circuits. Besides, current quantum-based methods ignore theoretical analysis which are essential for understanding the model performance and applying for downstream tasks such as reasoning, path query answering, complex query answering, etc. To address measurement issue and bridge theory gap, we propose QubitE whose score of a triple is defined as the similarity between qubit states. Here, our measurements are viewed as kernel methods to separate the qubit states, while preserving quantum adavantages. Furthermore, we show that (1) QubitE is full-expressive; (2) QubitE can infer various relation patterns including symmetry/antisymmetry, inversion, and commutative/non-commutative composition; (3) QubitE subsumes serveral existing approaches, \eg~DistMult, pRotatE, RotatE, TransE and ComplEx; (4) QubitE owns linear space complexity and linear time complexity. Experiments results on multiple benchmark knowledge graphs demonstrate that QubitE can achieve comparable results to the state-of-the-art classical models.

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