𝐓𝐮𝐫𝐧𝐢𝐧𝐠 𝐍𝐚𝐭𝐮𝐫𝐚𝐥 𝐋𝐚𝐧𝐠𝐮𝐚𝐠𝐞 𝐢𝐧𝐭𝐨 𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐂𝐢𝐫𝐜𝐮𝐢𝐭𝐬: 𝐀 𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐚𝐥 𝐈𝐧𝐭𝐫𝐨𝐝𝐮𝐜𝐭𝐢𝐨𝐧 𝐭𝐨 𝐏𝐫𝐞𝐠𝐫𝐨𝐮𝐩 𝐆𝐫𝐚𝐦𝐦𝐚𝐫, 𝐃𝐢𝐬𝐂𝐨𝐏𝐲, 𝐚𝐧𝐝 𝐋𝐚𝐦𝐛𝐞𝐪

Quantum Natural Language Processing (QNLP) sits at the intersection of linguistics, category theory, and quantum computing. Instead of treating language as a sequence of tokens, QNLP views meaning as a compositional structure — something that can be represented diagrammatically and then interpreted as a quantum process. This article provides a compact technical walkthrough of how a simple sentence can be transformed into a categorical diagram using Pregroup Grammar and then compiled into a quantum circuit using lambeq. The process begins with part-of-speech tagging using spaCy, which identifies noun and verb tokens in a sentence. In Pregroup Grammar, each word is assigned a type based on its grammatical function. Nouns are given the atomic type n, sentences the type s, and transitive verbs are represented by the compound type

𝑛 ^𝑟 ⋅ 𝑠 ⋅ 𝑛^ 𝑙 ,

meaning they require a noun on both sides to form a valid sentence. These types are modeled using DisCoPy’s Ty and Word objects. Once the words are typed, DisCoPy constructs a string diagram representing their grammatical composition. Cups are introduced to contract matching adjoint types: one cup connects the subject noun with the verb’s left adjoint, and another connects the object noun with the verb’s right adjoint. This reduction mirrors grammatical correctness: if all adjoints cancel cleanly, the resulting diagram yields the sentence type s, indicating a well-formed structure. After the grammatical diagram is built, lambeq translates it into its own internal representation. This diagram is then passed to an ansatz — here an IQPAnsatz — which maps each atomic type to qubits and converts the diagram into a quantum circuit. The circuit encodes both structural and lexical information, allowing downstream tasks like classification, clustering, or semantic similarity to be performed on quantum hardware or simulators. By mapping language into compositional quantum processes, QNLP offers a principled, mathematically aligned alternative to embedding-based NLP models, especially for tasks sensitive to syntactic structure. This workflow demonstrates how linguistic structure, categorical reasoning, and quantum computation can seamlessly interoperate. It highlights the elegance of using monoidal categories as a unifying language across grammar and quantum circuits, forming the backbone of emerging quantum-native NLP technologies. A simple implementation with explanations can be found in this video link

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QNLP #QuantumComputing #DisCoPy #lambeq #CategoryTheory #Pregroup