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Every Scalar Accounted For: Exact meaning from a sentence to a quantum amplitude, and a road to language models native to quantum processors

The Institute for Applied Ontological Mathematics, Richard Goodman

Published Oct 12, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.33346.34244

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The Categorical Compositional Distributional (DisCoCat) model has been proven to be very successful in modelling sentence meaning as the interaction of word meanings. Words are modelled as quantum states, interacting guided by grammar. This model of language has been extended to density matrices to account for ambiguity in language. Density matrices describe probability distributions over quantum states, and in this work we relate the mixedness of density matrices to ambiguity in the sentences they represent. The von Neumann entropy and the fidelity are used as measures of this mixedness. Via the process of amplitude encoding, we introduce classical data into quantum machine learning algorithms. First, the findings suggest that in quantum natural language processing, amplitude-encoding data onto a quantum computer can be a useful tool to improve the performance of the quantum machine learning models used. Second, the effect that these encoded data have on the above-introduced relation between entropy and ambiguity is investigated. We conclude that amplitude-encoding classical data in quantum machine learning algorithms makes the relation between the entropy of a density matrix and ambiguity in the sentence modelled by this density matrix much more intuitively interpretable.
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks and quantum circuits. DisCoCat diagrams have been connected to density matrices in various contexts in Quantum Natural Language Processing (QNLP). Previous use of density matrices in QNLP entails modelling ambiguous words as probability distributions over basic words (e.g., the word queen might mean the reigning queen or the chess piece). In this article, we investigate the use of probability distributions over processes to account for syntactic ambiguity in sentences. The meanings of these sentences are represented by density matrices. We show how to create probability distributions on quantum circuits that represent the meanings of sentences and explain how this approach generalises tasks from the literature. We report on a proof-of-concept experiment to demonstrate the proposed theory.
As part of the recent research effort on quantum natural language processing (QNLP), variational quantum sentence classifiers (VQSCs) have been implemented and supported in lambeq / DisCoPy, based on the DisCoCat model of sentence meaning. We discuss in some detail VQSCs, including category theory, DisCoCat for modeling sentence as string diagram, and DisCoPy for encoding string diagram as parameterized quantum circuit. Many NLP tasks, however, require the handling of text consisting of multiple sentences, which is not supported in lambeq / DisCoPy. A good example is sentiment classification of customer feedback or product review. We discuss three potential approaches to variational quantum text classifiers (VQTCs), in line with VQSCs. The first is a weighted bag-of-sentences approach which treats text as a group of independent sentences with task-specific sentence weighting. The second is a coreference resolution approach which treats text as a consolidation of its member sentences with coreferences among them resolved. Both approaches are based on the DisCoCat model and should be implementable in lambeq / DisCoCat. The third approach, on the other hand, is based on the DisCoCirc model which considers both ordering of sentences and interaction of words in composing text meaning from word and sentence meanings. DisCoCirc makes fundamental modification of DisCoCat since a sentence in DisCoCirc updates meanings of words, whereas all meanings are static in DisCoCat. It is not clear if DisCoCirc can be implemented in lambeq / DisCoCat without breaking DisCoCat.