A quantum-inspired version of the nearest mean classifier

We introduce a framework suitable for describing standard classification problems using the mathematical language of quantum states. In particular, we provide a one-to-one correspondence between real objects and pure density operators. This correspondence enables us: (1) to represent the nearest mean classifier (NMC) in terms of quantum objects, (2) to introduce a quantum-inspired version of the NMC called quantum classifier (QC). By comparing the QC with the NMC on different datasets, we show how the first classifier is able to provide additional information that can be beneficial on a classical computer with respect to the second classifier

PhysicSpace: From Quantum to Human Scale

We describe a month-long project about communicating physics concepts and methods through spatial and experiential installations in a public exhibition. A collaboration between MA students in Information Experience Design at the Royal College of Art and physics PhD students at Imperial College London resulted in an exhibition which rendered quantum interactions of particles and fluids at human scale using wood, lasers, projections, lenticular printing and digital technologies, in an atmospheric underground space in May 2014. This work, we believe, signals a new category of art-science collaborations, in between didactic museum displays, practical visualisations, and science-inspired art projects, aimed at communicating scientific concepts spatially, experientially and with artistic methods and critical narratives

Quantum Cognitively Motivated Decision Fusion for Video Sentiment Analysis

Video sentiment analysis as a decision-making process is inherently complex, involving the fusion of decisions from multiple modalities and the so-caused cognitive biases. Inspired by recent advances in quantum cognition, we show that the sentiment judgment from one modality could be incompatible with the judgment from another, i.e., the order matters and they cannot be jointly measured to produce a final decision. Thus the cognitive process exhibits "quantum-like" biases that cannot be captured by classical probability theories. Accordingly, we propose a fundamentally new, quantum cognitively motivated fusion strategy for predicting sentiment judgments. In particular, we formulate utterances as quantum superposition states of positive and negative sentiment judgments, and uni-modal classifiers as mutually incompatible observables, on a complex-valued Hilbert space with positive-operator valued measures. Experiments on two benchmarking datasets illustrate that our model significantly outperforms various existing decision level and a range of state-of-the-art content-level fusion approaches. The results also show that the concept of incompatibility allows effective handling of all combination patterns, including those extreme cases that are wrongly predicted by all uni-modal classifiers.Comment: The uploaded version is a preprint of the accepted AAAI-21 pape

Human Perception as a Phenomenon of Quantization

For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of 'categorical perception' has put us on track to find a possible deeper cause of the presence of this quantum structure in human cognition. Thus, we show that in an archetype of human perception consisting of the reconciliation of a bottom up stimulus with a top down cognitive expectation pattern, there arises the typical warping of categorical perception, where groups of stimuli clump together to form quanta, which move away from each other and lead to a discretization of a dimension. The individual concepts, which are these quanta, can be modeled by a quantum prototype theory with the square of the absolute value of a corresponding Schr\"odinger wave function as the fuzzy prototype structure, and the superposition of two such wave functions accounts for the interference pattern that occurs when these concepts are combined. Using a simple quantum measurement model, we analyze this archetype of human perception, provide an overview of the experimental evidence base for categorical perception with the phenomenon of warping leading to quantization, and illustrate our analyses with two examples worked out in detail.Comment: 28 pages, 8 figure

Quantum-Inspired Machine Learning: a Survey

Quantum-inspired Machine Learning (QiML) is a burgeoning field, receiving global attention from researchers for its potential to leverage principles of quantum mechanics within classical computational frameworks. However, current review literature often presents a superficial exploration of QiML, focusing instead on the broader Quantum Machine Learning (QML) field. In response to this gap, this survey provides an integrated and comprehensive examination of QiML, exploring QiML's diverse research domains including tensor network simulations, dequantized algorithms, and others, showcasing recent advancements, practical applications, and illuminating potential future research avenues. Further, a concrete definition of QiML is established by analyzing various prior interpretations of the term and their inherent ambiguities. As QiML continues to evolve, we anticipate a wealth of future developments drawing from quantum mechanics, quantum computing, and classical machine learning, enriching the field further. This survey serves as a guide for researchers and practitioners alike, providing a holistic understanding of QiML's current landscape and future directions.Comment: 56 pages, 13 figures, 8 table

Цветовая кодировка кубитных состояний

Difficulties in algorithmic simulation of natural thinking point to the inadequacy of information encodings used to this end. The promising approach to this problem represents information by the qubit states of quantum theory, structurally aligned with major theories of cognitive semantics. The paper develops this idea by linking qubit states with color as fundamental carrier of affective meaning. The approach builds on geometric affinity of Hilbert space of qubit states and color solids, used to establish precise one-to-one mapping between them. This is enabled by original decomposition of qubit in three non-orthogonal basis vectors corresponding to red, green, and blue colors. Real-valued coefficients of such decomposition are identical to the tomograms of the qubit state in the corresponding directions, related to ordinary Stokes parameters by rotational transform. Classical compositions of black, white and six main colors (red, green, blue, yellow, magenta and cyan) are then mapped to analogous superposition of the qubit states. Pure and mixed colors intuitively map to pure and mixed qubit states on the surface and in the volume of the Bloch ball, while grayscale is mapped to the diameter of the Bloch sphere. Herewith, the lightness of color corresponds to the probability of the qubit’s basis state «1», while saturation and hue encode coherence and phase of the qubit, respectively. The developed code identifies color as a bridge between quantum-theoretic formalism and qualitative regularities of the natural mind. This opens prospects for deeper integration of quantum informatics in semantic analysis of data, image processing, and the development of nature-like computational architectures.Трудности алгоритмической имитации естественного мышления указывают на несовершенство используемых для этого форматов представления информации. В этом отношении перспективна кодировка информации кубитными состояниями квантовой теории, структура которых согласуется с крупными теориями когнитивной семантики. Представлено развитие этого подхода, связывающее кубитные состояния с цветом как самостоятельным носителем эмоционально-смысловых значений. Основой для этого стало геометрическое подобие цветовых тел и Гильбертова пространства кубитных состояний, позволившее установить между ними взаимооднозначное математическое отображение. Для этого использовано оригинальное разложение кубита по тройке неортогональных векторов, соответствующих красному, синему и зелёному цветам. Действительные коэффициенты такого разложения являются томограммами кубитного состояния по соответствующим направлениям, связанными с компонентами вектора Стокса операцией поворота. При этом композиционные соотношения чёрного, белого и шести основных цветов (красный, зелёный, синий, жёлтый, фиолетовый, голубой) выражаются аналогичными суперпозициями кубитных состояний. Чистые и смешанные цвета соответствуют чистым и смешанным состояниям на поверхности и внутри сферы Блоха, тогда как оттенки серого отображаются на вертикальный диаметр сферы. При этом светлость цвета соответствует вероятности базисного кубитного состояния «1», тогда как насыщенность цвета и цветовой тон кодируют когерентность и фазу кубитного состояния. Полученный результат открывает возможности для использования квантовой информатики в задачах семантического анализа данных, обработки изображений и создания природоподобных вычислительных архитектур