At the heart of creativity is the forging of new concept combinations and the adapting of existing ideas to new situations. However, these processes have resisted mathematical description; concepts violate the rules of classical logic when they interact, e.g., concept combinations can exhibit emergent features not possessed by their constituent concepts. These challenges can be addressed using the quantum cognition framework, wherein nonclassical behavior is described in terms of superposition, entanglement, and interference. While in classical probability theory events are drawn from a common sample space, in quantum models events are defined only with respect to a measurement, or (in quantum cognition) a context, and the probabilities reflect the underlying reality. The measurement (or context) causes collapse from a superposition state to a definite eigenstate. The paper explains how creativity can be modelled using quantum cognition approach with an illustrative example, and discuss how the approach could be implemented computationally. Quantum computing is widely expected to revolutionize many fields in the near future through immense increases in speed and computing power. The time may be ripe to explore the potential of quantum computational creativity.
At the heart of creativity is the forging of new concept combinations and the adapting of existing ideas to new situations. However, these processes have resisted mathematical description; concepts violate the rules of classical logic when they interact, e.g., concept combinations can exhibit emergent features not possessed by their constituent concepts. These challenges can be addressed using the quantum cognition framework, wherein nonclassical behavior is described in terms of superposition, entanglement, and interference. While in classical probability theory events are drawn from a common sample space, in quantum models events are defined only with respect to a measurement, or (in quantum cognition) a context, and the probabilities reflect the underlying reality. The measurement (or context) causes collapse from a superposition state to a definite eigenstate. The paper explains how creativity can be modelled using quantum cognition approach with an illustrative example, and discuss how the approach could be implemented computationally. Quantum computing is widely expected to revolutionize many fields in the near future through immense increases in speed and computing power. The time may be ripe to explore the potential of quantum computational creativity.
The representation and processing of concepts is one of the hardest challenges in cognitive science. While computer scientists and engineers have focused on developing advances for particular tasks, philosophers and cognitive scientists have focused on elucidating the structural nature of meaning. A remarkable bridge between these two limited-success approaches can be found in behavioral research, since, in a variety of tasks, humans process information at a conceptual level in a way that is incompatible with classical probability and fuzzy set theory. Recently, attempts have been made to use mathematical schemes founded on quantum structures as alternative approaches. For this reason, the application of quantum structures to this type of phenomena has received increasing attention. The quantum approach allows to faithfully model a number of non-classical deviations observed in experimental data. Moreover, it shows that genuine quantum theoretical notions, such as contextuality, superposition, emergence, and entanglement, are powerful epistemic tools to understand and represent cognitive phenomena. In this thesis, we identify the limitations of classical theories to handle some important cognitive tasks, and introduce the fundamentals of the quantum cognitive approach to concepts. Next, we perform a mathematical analysis of current concept combination models and develop an extension that allows for concrete representations of multiple exemplars simultaneously. Our analysis indicates that a superposition of logical reasoning and a specific form of non-logical reasoning, where non-logical reasoning is dominant, allows to faithfully represent the experimental data. Therefore, the non-logical reasoning introduced by this model represents an important but unexplored form of reasoning in humans. In addition, we develop novel experimental methodologies to identify quantum conceptual structures for concept combinations in the context of natural language processing and psychological experiments. Namely, we present a methodology to build entangled concepts represented as sets of words with respect to a corpus of text, and present a computational and psychological methodology to discern if a collection of concepts behaves statistically as a collection of quantum or classical particles. Using both methodologies we have identified a significant presence of quantum conceptual structure in the context of natural language processing and psychological experiments.
The emergence of quantum computing has prompted researchers to examine potential parallels between quantum mechanical principles and human cognitive processes. This article explores the theoretical framework of quantum cognition, examining how concepts from quantum mechanics, including superposition, entanglement, and measurement, might inform our understanding of human decision-making, memory, and consciousness. While quantum computing operates on fundamentally different physical principles than biological neural networks, the mathematical formalisms of quantum mechanics offer novel perspectives on cognitive phenomena that classical probability theory struggles to explain. This review critically examines the current state of quantum cognition research, its applications in computational modeling, and the ongoing debates regarding the validity of quantum mechanical analogies in psychological theory. The analysis reveals both promising theoretical insights and significant limitations in applying quantum principles to human cognition, highlighting the need for empirical validation and careful distinction between mathematical analogy and physical reality.
The increasing complexity of modern decision-making environments has challenged the effectiveness of classical mathematical models. Traditional probabilistic frameworks often struggle to represent uncertainty, ambiguity, contextual dependence, and nonlinear interactions among decision variables. Quantum-inspired mathematical models have emerged as a promising interdisciplinary approach that leverages mathematical principles derived from quantum theory without requiring quantum computing hardware. These models utilize concepts such as superposition, interference, entanglement, and contextuality to represent complex decision processes more accurately. This paper explores the theoretical foundations, mathematical structures, and applications of quantum-inspired decision models in complex systems. The study examines how quantum probability theory provides a more flexible representation of human cognition, organizational decision-making, financial forecasting, and artificial intelligence systems. Furthermore, the paper discusses mathematical formulations, implementation strategies, advantages, challenges, and future research directions. The findings suggest that quantum-inspired models offer significant potential for addressing uncertainty and dynamic interactions in complex decision environments, thereby contributing to the advancement of intelligent decision support systems.
We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.
This review presents an overview of cognitive systems, quantum phenomena and possible connections between them. The focus will be the artificial cognitive systems and briefly touch the discussion of possible benefits from quantum counterparts. The nonclassical features of Quantum Theory introduced as quantum resources which enables possible speed ups or advantages over classical computational tasks. Quantum computation is introduced as a powerful computational tool over its classical counterparts by also covering possible applications of cognitive phenomena in the framework of quantum cognition. Also different attempts in order to implement decision making processes for cognitive purposes mentioned.
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.