知识图的量子机器学习算法
Quantum Machine Learning Algorithm for Knowledge Graphs
摘要：
语义知识图是用于知识表示和推理的大规模三元数据库。隐含知识可以通过建模和重构从知识图生成的张量表示来推断。然而，随着知识图的规模不断增长，经典建模变得越来越计算资源密集。本文研究了如何利用量子资源来加速知识图的建模。特别是，我们提出了第一个量子机器学习算法，用于对张量化数据进行推理，例如，知识图谱由于大多数张量问题都是NP困难的，因此设计量子算法来支持这项任务是具有挑战性的。我们简化了问题，提出一个合理的假设，张量表示的知识图可以近似其低秩张量奇异值分解，这是由我们的实验验证。所提出的基于采样的量子算法实现了指数加速，其运行时间在知识图张量的维度上是多对数的。
英文摘要：
Semantic knowledge graphs are large-scale triple-oriented databases for knowledge representation and reasoning. Implicit knowledge can be inferred by modeling and reconstructing the tensor representations generated from knowledge graphs. However, as the sizes of knowledge graphs continue to grow, classical modeling becomes increasingly computational resource intensive. This paper investigates how quantum resources can be capitalized to accelerate the modeling of knowledge graphs. In particular, we propose the first quantum machine learning algorithm for making inference on tensorized data, e.g., on knowledge graphs. Since most tensor problems are NP-hard, it is challenging to devise quantum algorithms to support that task. We simplify the problem by making a 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 exponential speedup with a runtime that is polylogarithmic in the dimension of knowledge graph tensor.
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