The conceptual model and mathematical formalism of quan-tum theory are employed in creating a novel framework for modeling the computational search process addressing problematic issues that restrict information retrieval research. Mapping the mathematical formalism of search to that of quantum theory presents insightful perspectives about the na-ture of search. However, differences in operational semantics of quantum theory and search restrict the utility of the map-ping. An approach is suggested for resolving these semantic differences aiming toward a sound mathematical and concep-tual framework for search inspired by quantum theory.
The conceptual model and mathematical formalism of quan-tum theory are employed in creating a novel framework for modeling the computational search process addressing problematic issues that restrict information retrieval research. Mapping the mathematical formalism of search to that of quantum theory presents insightful perspectives about the na-ture of search. However, differences in operational semantics of quantum theory and search restrict the utility of the map-ping. An approach is suggested for resolving these semantic differences aiming toward a sound mathematical and concep-tual framework for search inspired by quantum theory.
Since 2004, researchers have been using the mathematical framework of quantum theory in information retrieval (IR). Quantum theory offers a generalized probability and logic framework. Such a framework has been shown to be capable of unifying the representation, ranking, and user cognitive aspects of IR, and helpful in developing more dynamic, adaptive, and context-aware IR systems. Although quantum-inspired IR is still a growing area, a wide array of work in different aspects of IR has been done and produced promising results. This article presents a survey of the research done in this area, aiming to show the landscape of the field and draw a road map of future directions.
September 2006Abstract: Traditional database query languages are based on set theory and crisp first order logic. However, many applications require retrieval-like queries which return result objects associated with a degree value of being relevant to the query. Traditionally, retrieval systems estimate relevance by exploiting hidden object semantics whereas query processing in database systems relies on matching select-conditions with attribute values. Thus, different mechanisms were developed for database and information retrieval systems. In consequence, there is a lack of support for queries involving both retrieval and database search terms. In this work, we develop a unifying framework based on the mathematical formalism of quantum mechanics and quantum logic. Van Rijsbergen already discussed the strong relation between the formalism of quantum mechanics and information retrieval. The goal of this work is to interrelate concepts from database query processing to concepts from quantum mechanics and logic. As result, we obtain a common theory which allows us to incorporate seamlessly retrieval search into traditional database query processing. Exploiting our theoretical results, we introduce the quantum query language QQL. In contrast to competing approaches, our formalism is based on quantum logic.
In the previous article, we presented a quantum-inspired framework for modeling semantic representation and processing in Large Language Models (LLMs), drawing upon mathematical tools and conceptual analogies from quantum mechanics to offer a new perspective on these complex systems. In this paper, we clarify the core assumptions of this model, providing a detailed exposition of six key principles that govern semantic representation, interaction, and dynamics within LLMs. The goal is to justify that a quantum-inspired framework is a valid approach to studying semantic spaces. This framework offers valuable insights into their information processing and response generation, and we further discuss the potential of leveraging quantum computing to develop significantly more powerful and efficient LLMs based on these principles.
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted by assuming the existence in human thought of a double-layered structure, a 'classical logical thought' and a 'quantum conceptual thought', the latter being responsible of the above paradoxes and nonclassical effects. The presence of a quantum structure in cognition is relevant, for it shows that quantum mechanics provides not only a useful modeling tool for experimental data but also supplies a structural model for human and artificial thought processes. This approach has strong connections with theories formalizing meaning, such as semantic analysis, and has also a deep impact on computer science, information retrieval and artificial intelligence. More specifically, the links with information retrieval are discussed in this paper.
Quantum theory poses deep challenges to the mechanical conception of reality that underlies classical physics. Yet today, over eighty years after its creation, its implications for our picture of reality remain enshrouded in uncertainty. In view of the current search for a more comprehensive theory of physics (a so-called theory of everything), it is vital that these implications be clearly elucidated. In this article, I describe the nature of the challenge posed by quantum theory, and outline efforts that have been made to better understand its nonclassical features, such as non-locality. In particular, I discuss the informational perspective, which, through the study of quantum information processing, has provided deep insights into the nature of quantum reality, and has also revitalized the long-standing quest to reconstruct the content of the rather mysterious mathematical formalism of quantum theory from a set of crisp physical principles. Finally, I indicate some implications of recent reconstructive work for the search for a theory of quantum gravity, and, more broadly, for our picture of physical reality.
The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval. In this paper, we overview the quantum cognition approach developed in our Brussels team during the last two decades, specifically our identification of quantum structures in human concepts and language, and the modeling of data from psychological and corpus-text-based experiments. We discuss our quantum-theoretic framework for concepts and their conjunctions/disjunctions in a Fock-Hilbert space structure, adequately modeling a large amount of data collected on concept combinations. Inspired by this modeling, we put forward elements for a quantum contextual and meaning-based approach to information technologies in which 'entities of meaning' are inversely reconstructed from texts, which are considered as traces of these entities' states.