# Quantum Natural Language Processing: Challenges and Opportunities
## 2 Theoretical Background
### NLP and Quantum: The Meeting Point  
One of the assumptions underlying the union between natural language processing and quantum theory is the possibility of creating a direct relationship between linguistic features (i.e., syntactic structures and semantics meanings) and quantum states. This is made possible using the DisCoCat framework through string diagrams [36] as a network-like language [37]. This approach is part of a long and flourishing tradition of computational linguistics focused on the search for the most efficient way to represent language structures and meanings in a machine-readable way. On the one hand, the distributional approach--which has been the most successful line of research in recent years--relies on statistics about the contexts in which words occur according to the distributional hypothesis [38]. By contrast,the symbolic approach [39] has been focused on individual meanings that compose the sentence. This approach is based on the theoretical linguistics' concept of compositionality, arguing that the meaning of a sentence depends on the meanings of its parts and by the grammar according to which they are arranged together. Therefore, the analysis of the individual constituents determines the overall meaning, which is expressed using a formal logical language. This line of research has obtained less success in NLP applications so far. Current state-of-the-art neural network models are based on the dominant distributional paradigm. Therefore, this approach is not without problems. First, there is a big bottleneck created by the need for ever larger data sets and parameters; moreover, the interpretation of these models is difficult [40]. The first attempt to overcome the limitations of current NLP models is to include features about the structure of the language (basically syntax) into canonical distributional language models. The resulting model--denoted as DisCoCat--incorporates categorical information and distributional information. Note that this is certainly not a new approach in the field of theoretical and computational linguistics, since its roots lie in the Universal Grammar [41] and foundational work of [42,43], while applied aspects come from categorical grammars proposed by [44] and pregroup grammar [45]. The Compositional Distributional Model  
Given the premise that the constituents of a sentence are strongly interconnected, and the grammatical structures in which they are involved affect semantics [46], the pioneering work proposed by [25] has proposed a graphical framework to draw string diagrams (see Figure 1) exploiting concepts from [PERSON]'s pregroup grammar [47]. The uniqueness of the proposed representation is that sentence meanings can be totally independent of the grammatical structure. The question they intended to answer is not only rooted in compositionality, i.e., whether the meaning of a whole sentence can be deduced by single meanings of its words. The aim is rather to make the first steps towards a grammar-informed NLP, deepening the ways in which words interact with each other and establishing their meanings. In other terms, the framework aims to combine in a whole diagrammatic representation structural aspects of language (grammar theory and syntax) and statistical approaches based on empirical evidences (machine/deep learning). In the diagram, boxes represent meanings of words that are transmitted via wires. It deals with a representation similar to the canonical Dependency Parse Tree (DPT) well known in the linguistics literature, but it does not introduce a hierarchical tree structure. In the example shown in Figure 1, the noun in subject position \"Max\" and the one in object position \"pizza\" are both related with the verb \"ate\" and the combination of these words builds up the meaning of the overall sentence. In this way, distributional and compositional aspects are combined into DisCoCat. The meaning of sentences is computed using pregroup grammar via tensor product composition.