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![The Bloch sphere as a Betweenness space, with marked examples of betweenness B(x, y, z), and a convex region shown in purple. The states |ψi⟩⟨ψi|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{\psi _i}\rangle \langle {\psi _i}|$$\end{document} are used to show that |0⟩⟨0|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{0}\rangle \langle {0}|$$\end{document} is not quasi-concave](publication/379835331/figure/fig1/AS:11431281255804546@1719436030509/The-Bloch-sphere-as-a-Betweenness-space-with-marked-examples-of-betweenness-Bx-y-z.png)
The Bloch sphere as a Betweenness space, with marked examples of betweenness B(x, y, z), and a convex region shown in purple. The states |ψi⟩⟨ψi|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{\psi _i}\rangle \langle {\psi _i}|$$\end{document} are used to show that |0⟩⟨0|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|{0}\rangle \langle {0}|$$\end{document} is not quasi-concave
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In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very different instantiations: one classical and one quantum. A contribution of the work is a thorough category-the...
Citations
... By fostering a culture of innovation and resilience, the quantum strategic vision aims to create a sustainable energy future that is both environmentally responsible and economically viable, ensuring that energy systems are prepared to meet the needs of generations to come. A "quantum strategic vision" in architecture reimagines space by applying principles from quantum physics to enhance both functionality and aesthetic experience [22]. This vision aims to harness quantum concepts-such as energy flux, dynamic interactions, and spatial adaptability-to create architectural spaces that feel responsive and alive [23]. ...
Designing spaces that promote occupant health and well-being is essential to achieve sustainable building practices. This paper considers a sustainable architecture design by investigating quantum energy and perception within architectural space. To this end, the mutual influence between the building and the user through the energy effect of space is investigated. Besides, this paper discusses the energy's role in architecture and the nature of perception in shaping spatial awareness and human engagement within environments. In addition, this paper discuss how quantum and electromagnetic energy can enhance architectural design. We aim to provide information related to the study of the magnetic field effect in architecture design, specifically the effect of the geomagnetic field on occupants. Examples of practical implementation have been presented with the aim to provide effective recommendations for future architectural design. The findings in this research highlight the potential of energy-inspired designs to create built environments that are both more sustainable and adaptive.
... Logical and conversational negation has also been studied in the context of quantum models [Lew20,RSY21]. Ref. [TSZC24] investigates how a category-theoretic treatment of conceptual spaces [Gär14] can be instantiated with a (hybrid) quantum model, showing how a CNN can be trained to predict the parameters of a PQC representing the colour, size, shape and position of a simple image. ...
We present a variety of methods for training complex-valued word embeddings, based on the classical Skip-gram model, with a straightforward adaptation simply replacing the real-valued vectors with arbitrary vectors of complex numbers. In a more "physically-inspired" approach, the vectors are produced by parameterised quantum circuits (PQCs), which are unitary transformations resulting in normalised vectors which have a probabilistic interpretation. We develop a complex-valued version of the highly optimised C code version of Skip-gram, which allows us to easily produce complex embeddings trained on a 3.8B-word corpus for a vocabulary size of over 400k, for which we are then able to train a separate PQC for each word. We evaluate the complex embeddings on a set of standard similarity and relatedness datasets, for some models obtaining results competitive with the classical baseline. We find that, while training the PQCs directly tends to harm performance, the quantum word embeddings from the two-stage process perform as well as the classical Skip-gram embeddings with comparable numbers of parameters. This enables a highly scalable route to learning embeddings in complex spaces which scales with the size of the vocabulary rather than the size of the training corpus. In summary, we demonstrate how to produce a large set of high-quality word embeddings for use in complex-valued and quantum-inspired NLP models, and for exploring potential advantage in quantum NLP models.
