A Quantum Expectation Value Based Language Model with Application to Question Answering

Quantum-inspired language models have been introduced to Information Retrieval due to their transparency and interpretability. While exciting progresses have been made, current studies mainly investigate the relationship between density matrices of difference sentence subspaces of a semantic Hilbert space. The Hilbert space as a whole which has a unique density matrix is lack of exploration. In this paper, we propose a novel Quantum Expectation Value based Language Model (QEV-LM). A unique shared density matrix is constructed for the Semantic Hilbert Space. Words and sentences are viewed as different observables in this quantum model. Under this background, a matching score describing the similarity between a question-answer pair is naturally explained as the quantum expectation value of a joint question-answer observable. In addition to the theoretical soundness, experiment results on the TREC-QA and WIKIQA datasets demonstrate the computational efficiency of our proposed model with excellent performance and low time consumption.