# Quantum Natural Language Processing: Challenges and Opportunities
## 5 Quantum-Inspired Approaches
### Information Retrieval  
One of the first approaches advocating the use of Quantum Theory for an NLP task has been proposed by [53]. In this work, the quantum probabilistic framework is used to develop a general approach to the information retrieval task. A density matrix has been used to represent texts and term dependencies in a quantum language model (QLM), combining the flexibility of vector spaces with probabilistic calculus. Dependencies are not more represented stochastically as joined probabilities but as superposition events, i.e., additional dimensions. The experiments have compared the proposed QLM to the baseline unigram language model, based on a bag-of-words approach, in particular Dirichlet smoothing, and to the full dependence version of the non bag-of-words MRF model. Tests have been made on different datasets (SJMN, TREC7-8, WT10g and ClueWeb-B) using the mean average precision (MAP) as metric. QLM consistently achieves results above baseline, with MAP increments varying from 12% to 19% depending on the dataset used. A similar work [54] has proposed to introduce the quantum entanglement in order to improve the performance of QLM in the information retrieval task. The basic assumption underlying this approach is the equivalence between quantum entanglement (QE) with a traditional retrieval approach, in this case Unconditional Pure Dependence (UDP) [78] used in the Markov Random Field (MRF) retrieval model [79]. Starting from this, the occurrence of QE can be inferred extracting UDP patterns. After that, the QLM has been enhanced using QE, producing a new quantum-entanglement model for information retrieval (QQE). This enhanced model has been shown to achieve better performance than both the traditional model (MRE) and the QML. MAP has been used as metric to evaluate retrieval performance on five collections in the documents' re-ranking task. However, performance has been \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Task** & **Proposed Approach** & **Dataset** & **Metric** & **Score** \\ \hline \multirow{6}{*}{Information retrieval} & \multirow{3}{*}{Quantum Language Model (QLM) [53]} & SJMN & & 0.2093 (0.271) \\  & & TREC7-8 & & 0.2254 (0.2243) \\  & & WT10g & & 0.2264 (0.2146) \\  & & ClueWeb-B & & 0.1196 (0.1137) \\ \cline{2-5}  & \multirow{2}{*}{Quantum Language Model-based Query Expansion (QLM-QE) [55]} & TREC 2013 & \multirow{2}{*}{MAP@10} & 8.94 (4.91) \\  & & TREC 2014 & & 14.79 (14.52) \\ \cline{2-5}  & \multirow{2}{*}{Quantum Interference-inspired Neural Matching model (QINQ) [56]} & ClueWeb-B & \multirow{2}{*}{MAP} & 0.134 (0.082) \\  & & Robust-Q4 & & 0.294 (0.103) \\ \hline \multirow{6}{*}{Question answering} & Neural Network-based Quantum-like Language Model (NNQLM) [57] & TREC-QA & \multirow{2}{*}{MAP} & 0.758 (0.678) \\  & & WIKQA & & 0.649 (0.510) \\ \cline{2-5}  & \multirow{2}{*}{Quantum Many-body Wave Function for Language Modeling (QMWF-LM) [58]} & TREC-QA & \multirow{2}{*}{MAP} & 0.752 (0.678) \\  & & WIKQA & & 0.695 (0.512) \\ \cline{2-5}  & \multirow{2}{*}{Complex-valued-Network (CNM) [59]} & YahooQA & \multirow{2}{*}{MAP} & 0.575 (0.395) \\  & & TREC-QA & & 0.770 (0.777) \\  & & WIKQA & & 0.674 (0.652) \\ \hline \multirow{6}{*}{Sentiment classification} & \multirow{3}{*}{GQLM [60]} & OMD & \multirow{3}{*}{Accuracy} & 0.629 (0.614) \\  & & SS-tweet & & 0.618 (0.579) \\ \cline{1-1} \cline{2-5}  & \multirow{2}{*}{Quantum-inspired Interactive Networks (QIN) [61]} & MED & \multirow{2}{*}{IEOCCAP} & 0.679 (0.652) \\  & & IEMOCAP & & 0.376 (0.351) \\ \cline{1-1} \cline{2-5}  & & MR & & 82.2 (82.3) \\ \cline{1-1}  & & CR & & 85.7 (85.4) \\ \cline{1-1}  & & Subj & & 95.3 (94.6) \\ \cline{1-1}  & & MPQA & & 90.4 (90.4) \\ \hline \multirow{2}{*}{BERT + TextTN [62]} & SST-2 & \multirow{2}{*}{Accuracy} & 95.3 (96.7) \\  & & SST-5 & & 54.8 (54.7) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of quantum-inspired approaches running on classical hardware.