Large language models (LLMs) achieve remarkable predictive capabilities but remain opaque in their internal reasoning, creating a pressing need for more interpretable artificial intelligence. Here, we propose bridging this explanatory gap by drawing on concepts from topological quantum computing (TQC), specifically the anyonic frameworks arising from SU(2)k theories. Anyons interpolate between fermions and bosons, offering a mathematical language that may illuminate the latent structure and decision-making processes within LLMs. By examining how these topological constructs relate to token interactions and contextual dependencies in neural architectures, we aim to provide a fresh perspective on how meaning and coherence emerge. After eliciting insights from ChatGPT and exploring low-level cases of SU(2)k models, we argue that the machinery of modular tensor categories and topological phases could inform more transparent, stable, and robust AI systems. This interdisciplinary approach suggests that quantum-theoretic principles may underpin a novel understanding of explainable AI.
Large language models (LLMs) achieve remarkable predictive capabilities but remain opaque in their internal reasoning, creating a pressing need for more interpretable artificial intelligence. Here, we propose bridging this explanatory gap by drawing on concepts from topological quantum computing (TQC), specifically the anyonic frameworks arising from SU(2)k theories. Anyons interpolate between fermions and bosons, offering a mathematical language that may illuminate the latent structure and decision-making processes within LLMs. By examining how these topological constructs relate to token interactions and contextual dependencies in neural architectures, we aim to provide a fresh perspective on how meaning and coherence emerge. After eliciting insights from ChatGPT and exploring low-level cases of SU(2)k models, we argue that the machinery of modular tensor categories and topological phases could inform more transparent, stable, and robust AI systems. This interdisciplinary approach suggests that quantum-theoretic principles may underpin a novel understanding of explainable AI.
This paper presents a novel framework that integrates artificial intelligence with superalgebraic structures to simulate topological quantum computation (TQC) in systems governed by Lie superalgebras such as osp(1∣2) and sl(2∣1). By combining symbolic algebra, modular tensor category theory, and generative AI models—including variational autoencoders and diffusion models—the proposed system enables accurate, scalable simulation of non-Abelian anyonic braiding and fusion operations within graded symmetry constraints. The framework encodes superalgebraic invariants and topological rules into neural architectures, allowing physically valid and symmetry-preserving generation of braid paths and fusion outcomes. Experimental results demonstrate high fidelity, topological consistency, and robustness against noise, with successful emulation on quantum hardware platforms such as IBM Q and IonQ. This research opens new avenues for fault-tolerant, algebraically informed quantum simulation, circuit synthesis, and adaptive control in next-generation quantum technologies. Keywords: topological quantum computation, superalgebra, Lie superalgebras, modular tensor categories, osp(1∣2), sl(2∣1), anyons, braiding, fusion rules, symbolic AI, generative models, quantum simulation, quantum invariants, diffusion models, fault-tolerant quantum computing
The rapid advancement of Artificial Intelligence (AI) has heightened concerns about the opacity of decision-making processes in complex models, particularly deep neural networks. This research explores a novel paradigm that integrates quantum computing principles into Explainable AI (XAI) to enhance interpretability without compromising predictive accuracy. The study introduces a Quantum-inspired Interpretable Model (QIIM) framework that leverages Hilbert space embeddings, unitary transformations, and operator-based learning to represent knowledge in a mathematically transparent form. The proposed model computes interpretability through the expectation values of observable operators, enabling the decomposition of decisions into quantifiable, human-understandable components. To capture hierarchical relationships, a Tensor Network Interpretable Model (TNIM) is further developed, offering scalable insights into complex dependencies among features. Experimental evaluations—performed on benchmark datasets for decision-making tasks—demonstrate that the quantum-inspired models achieve competitive accuracy while significantly improving local and global interpretability metrics compared to classical XAI techniques. The findings underscore the potential of quantum formalism as a new foundation for transparent AI systems, bridging the gap between computational efficiency and explainability. This study contributes to both theoretical understanding and practical advancement in interpretable machine learning, paving the way for ethically aligned, transparent, and human-trustworthy AI-driven decision support systems.
Large Language Models (LLMs) such as ChatGPT have transformed how we interact with and understand the capabilities of Artificial Intelligence (AI). However, the intersection of LLMs with the burgeoning field of Quantum Machine Learning (QML) is only in its nascent stages. This paper presents an exploration of this niche by detailing a comprehensive framework for implementing the foundational Transformer architecture -- integral to ChatGPT -- within a quantum computing paradigm. We meticulously design quantum circuits that implement adapted versions of the transformer's core components and the generative pre-training phase. By integrating quantum computing with LLMs, we aspire to open new avenues for research in QML and contribute to the ongoing evolution of AI technologies.
The increasing deployment of Artificial Intelligence (AI) systems across various domains necessitates a deeper understanding of their decision-making processes. Current explainable AI (XAI) techniques often struggle to provide truly transparent and reliable explanations, particularly for complex models like deep neural networks. This paper proposes a novel approach to algorithmic transparency and XAI leveraging concepts from quantum information theory. Specifically, we explore the potential of quantum entanglement and mutual information to represent and analyze AI model decisions in a fundamentally different way. Our framework represents model outputs as quantum states and investigates the correlations between these states and the input data. This analysis aims to identify the key factors driving the model's decision and provide a more intuitive and understandable explanation. We demonstrate that utilizing quantum information theory can offer a richer and more robust approach to XAI than traditional methods, potentially addressing limitations related to interpretability and trust in AI systems. This work lays the groundwork for a new paradigm in AI transparency, utilizing the unique properties of quantum mechanics to enhance the explainability of complex algorithms.
This paper proposes a bold conceptual framework: a deep mathematical unity exists among humancognition, quantum mechanics, and Large Language Models (LLMs). We argue that the foundationof cognition is language, and that the mathematical structure underlying language processing isanalogous to the matrix formulation of quantum mechanics. This framework providesa theoretical explanation for "why the Transformer architecture is so successful": LLMs donot accidentally simulate intelligence—they converge upon the underlying mathematical structure ofcognition itself.
We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT (GPT-5.5 Thinking) and Google Gemini Advanced (Gemini 1.5 Pro), we show that Bell's inequalities are significantly violated, which indicates the presence of a 'non-classical probability model' with probabilities that do not satisfy Kolmogorov's axioms. In the second test, also performed using ChatGPT and Gemini, we identify the presence of 'Bose-Einstein statistics', rather than the intuitively expected 'Maxwell-Boltzmann statistics', in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the 'systematic emergence of non-classical quantum-like structures in conceptual-linguistic domains', regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.