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arXiv:2507.02472 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Fast Variational Knowledge Graph Embedding

Pulak Ranjan Giri, Mori Kurokawa, Kazuhiro Saito

Published Sep 15, 2024• 0 citations
arXivHTMLPDF

Abstract

Embedding of a knowledge graph(KG) entities and relations in the form of vectors is an important aspect for the manipulation of the KG database for several downstream tasks, such as link prediction, knowledge graph completion, and recommendation. Because of the growing size of the knowledge graph databases, it has become a daunting task for the classical computer to train a model efficiently. Quantum computer can help speedup the embedding process of the KGs by encoding the entities into a variational quantum circuit of polynomial depth. Usually, the time complexity for such variational circuit-dependent quantum classical algorithms for each epoch is O(Npoly(logM)), where$N$is number of elements in the knowledge graph and$M$is the number of features of each entities of the knowledge graph. In this article we exploit additional quantum advantage by training multiple elements of KG in superpositions, thereby reducing the computing time further for the knowledge graph embedding model.

DOI
10.1109/qce60285.2024.10318

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Embedding of a knowledge graph(KG) entities and relations in the form of vectors is an important aspect for the manipulation of the KG database for several downstream tasks, such as link prediction, knowledge graph completion, and recommendation. Because of the growing size of the knowledge graph databases, it has become a daunting task for the classical computer to train a model efficiently. Quantum computer can help speedup the embedding process of the KGs by encoding the entities into a variational quantum circuit of polynomial depth. Usually, the time complexity for such variational circuit-dependent quantum classical algorithms for each epoch is O(Npoly(logM)), whereNNNis number of elements in the knowledge graph andMMMis the number of features of each entities of the knowledge graph. In this article we exploit additional quantum advantage by training multiple elements of KG in superpositions, thereby reducing the computing time further for the knowledge graph embedding model.
Knowledge graph is a collection of facts, known as triples(head, relation, tail), which are represented in form of a network, where nodes are entities and edges are relations among the respective head and tail entities. Embedding of knowledge graph for facilitating downstream tasks such as knowledge graph completion, link prediction, recommendation, has been a major area of research recently in classical machine learning. Because the size of knowledge graphs are becoming larger, one of the natural choices is to exploit quantum computing for knowledge graph embedding. Recently, a hybrid quantum classical model for knowledge graph embedding has been studied in which a variational quantum circuit is trained. One of the important aspects in knowledge graph embedding is the sampling of negative triples, which plays a crucial role in efficient training of the model. In classical machine learning various negative sampling strategies have been studied. In quantum knowledge graph embedding model, although we can use these strategies in principle, it is natural to ask if we can exploit quantum advantage in negative sampling. In this article we study such a negative sampling strategy, which exploits quantum superposition, and evaluate the model's performance with a knowledge graph database.
In this work, we propose the first quantum Ansätze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.
Knowledge graphs (KGs) are informative knowledge bases for various applications such as semantic web search or question answering. Since KGs often have missing facts mainly due to large construction costs, KG completion is a fundamental problem. Nowadays, as KGs have become large-scale, KG completion has become gradually intractable for classical computers. One promising direction is to utilize quantum circuits to capture complex structural information that entities and relations in KGs have. By encoding entities into quantum states and representing relations between entities as quantum circuits running on the quantum states, it becomes able to score and predict plausible missing entities or relations. However, it is still unclear how to design the quantum circuits to enhance KG completion accuracy. In this paper, we evaluate variations of quantum circuits in terms of KG completion accuracy, and investigate the relationship between the accuracy and the quality of the circuits (e.g., expressibility and entangling capacity). The experiments using a real KG show some correlation between the completion accuracy and the goodness of the circuits.
Quantum machine learning has made remarkable progress in many important tasks. However, the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms, making them non-end-to-end. Herein, we propose a quantum algorithm for the node embedding problem that maps a node graph’s topological structure to embedding vectors. The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms. With O(log(N)) qubits to store the information of N nodes, our algorithm will not lose quantum advantage for the subsequent quantum information processing. Moreover, owing to the use of a parameterized quantum circuit with O(poly(log(N))) depth, the resulting state can serve as an efficient quantum database. In addition, we explored the measurement complexity of the quantum node embedding algorithm, which is the main issue in training parameters, and extended the algorithm to capture high-order neighborhood information between nodes. Finally, we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.
Abstract In this work, the first quantum Ansätze for the statistical relational learning on knowledge graphs using parametric quantum circuits are proposed. Two types of variational quantum circuits for knowledge graph embedding are introduced. Inspired by the classical representation learning, latent features for entities are first considered as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, a second quantum circuit model is introduced where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. It is shown that the proposed methods can achieve comparable results to the state‐of‐the‐art classical models, for example, RESCAL , DistMult . Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.
Semantic knowledge graphs are large-scale triple-oriented databases for knowledge representation and reasoning. Implicit knowledge can be inferred by modeling the tensor representations generated from knowledge graphs. However, as the sizes of knowledge graphs continue to grow, classical modeling becomes increasingly computationally resource intensive. This article investigates how to capitalize on quantum resources to accelerate the modeling of knowledge graphs. In particular, we propose the first quantum machine learning algorithm for inference on tensorized data, i.e., on knowledge graphs. Since most tensor problems are NP-hard [18], it is challenging to devise quantum algorithms to support the inference task. We simplify the modeling task by making the plausible assumption that the tensor representation of a knowledge graph can be approximated by its low-rank tensor singular value decomposition, which is verified by our experiments. The proposed sampling-based quantum algorithm achieves speedup with a polylogarithmic runtime in the dimension of knowledge graph tensor.