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.

Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they serve as algebraic primitives that can be analysed without reference to input and can describe structures ranging from linear concepts to complicated manifolds. This work uses bilinear autoencoders to efficiently decompose representations into quadratic polynomials. We discuss improvements that induce importance ordering, clustering, and activation sparsity. This is an initial step toward nonlinear yet analysable latents through their algebraic properties.

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.