# Quantum Natural Language Processing: Challenges and Opportunities
## 3 Classification of Work
#### Pre-QNLP Approaches  
Even in its original pre-quantum formulation, the DisCoCat framework has had great success in the literature, as it was used for various linguistic phenomena. For instance, following an experiment proposed by [66], the work of [67] has tested DisCoCat on British National Corpus (BNC) [68] in order to demonstrate the possibility of a practical implementation of such a model opening the way to the production of large scale compositional models. More recently, other aspects connected to DisCoCat model have been investigated, including tasks such as negation and disambiguation. In particular, in [69] the possibility of a model for logical negation has been investigated. The work of [70] instead has proposed a method exploiting the distributional compositional categorical model of meaning to compare and translate sentences in English and Irish using via vector spaces.  
Afterwards, the tensor-network based approach on which DisCoCat is based has given rise to numerous derivative approaches. Among these, it is important to mention the study proposed by [71]. It has used the Frobenius algebra [72] to develop a compositional vector-based semantics of subject, and object relative pronouns within a categorical framework  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Type** & **Task** & **Work** \\ \hline \multirow{6}{*}{Theoretical approaches} & Syntactic-semantic & [PERSON] and [PERSON] (2016) [26] \\  & Representation & [PERSON] et al. (2020) [31] \\  & & [PERSON] et al. (2020) [49] \\ \cline{2-3}  & Disambiguation & \\  & Question answering & [PERSON] (2021) [51] \\ \cline{2-3}  & Machine translation & [PERSON] et al. (2021) [52] \\ \hline \multirow{6}{*}{Quantum-inspired approaches (classical hardware)} & \multirow{2}{*}{Information retrieval} & [PERSON] et al. (2013) [53] \\  & & [PERSON] et al. (2015) [54] \\  & & [PERSON] et al. (2018) [55] \\  & & [PERSON] et al. (2020) [56] \\ \cline{2-3}  & \multirow{2}{*}{Question answering} & [PERSON] et al. (2018) [57] \\  & & [PERSON] et al. (2018) [58] \\  & & [PERSON] et al. (2019) [59] \\ \cline{2-3}  & \multirow{2}{*}{Sentiment Analysis} & [PERSON] et al. (2018) [60] \\  & & [PERSON] et al. (2019) [61] \\  & & [PERSON] et al. (2020) [62] \\ \hline \multirow{6}{*}{Quantum computer approaches (NISQ hardware)} & Question answering & [PERSON] et al. (2020) [63] \\ \cline{2-3}  & Sentence classification & [PERSON] et al. (2021) [64] \\ \cline{1-1} \cline{2-3}  & Machine translation & [PERSON] (2021) [65] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of existing approaches divided by type (theoretical, really implemented on classical hardware and running on quantum hardware) and by NLP task on which they focused.  
have been supported. The general operations derived from the Frobenius algebra have been used to formalize the operations required to model the semantics of relative pronouns, ranging from relative clauses to modifiers. Again, the feasibility of the approach has been assessed through small-scale experiments on BNC corpus. Another work that has exploited tensor networks following DisCoCat idea has been proposed by [73]. It is a work focused on the disambiguation task. In particular, an algorithm able to improve number of tensor-based compositional distributional models of meaning introducing a step of disambiguation prior to composition has been developed. This approach is based on a methodology already known in the literature for automatic word sense disambiguation [74], which creates unambiguous versions of tensors before these are composed with vectors of nouns to construct vectors for sentences and phrases.