Algebraic Quantum Intelligence: A New Framework for Reproducible Machine Creativity
Kazuo Yano, Jonghyeok Lee, Tae Ishitomi, Hironobu Kawaguchi, Akira Koyama, Masakuni Ota, Yuki Ota, Nobuo Sato, Keita Shimada, Sho Takematsu, Ayaka Tobinai, Satomi Tsuji, Kazunori Yanagi, Keiko Yano, Manabu Harada, Yuki Matsuda, Kazunori Matsumoto, Kenichi Matsumura, Hamae Matsuo, Yumi Miyazaki, Kotaro Murai, Tatsuya Ohshita, Marie Seki, Shun Tanoue, Tatsuki Terakado, Yuko Ichimaru, Mirei Saito, Akihiro Otsuka, Koji Ara · Feb 15, 2026 · Citations: 0
Abstract
Large language models (LLMs) have achieved remarkable success in generating fluent and contextually appropriate text; however, their capacity to produce genuinely creative outputs remains limited. This paper posits that this limitation arises from a structural property of contemporary LLMs: when provided with rich context, the space of future generations becomes strongly constrained, and the generation process is effectively governed by near-deterministic dynamics. Recent approaches such as test-time scaling and context adaptation improve performance but do not fundamentally alter this constraint. To address this issue, we propose Algebraic Quantum Intelligence (AQI) as a computational framework that enables systematic expansion of semantic space. AQI is formulated as a noncommutative algebraic structure inspired by quantum theory, allowing properties such as order dependence, interference, and uncertainty to be implemented in a controlled and designable manner. Semantic states are represented as vectors in a Hilbert space, and their evolution is governed by C-values computed from noncommutative operators, thereby ensuring the coexistence and expansion of multiple future semantic possibilities. In this study, we implement AQI by extending a transformer-based LLM with more than 600 specialized operators. We evaluate the resulting system on creative reasoning benchmarks spanning ten domains under an LLM-as-a-judge protocol. The results show that AQI consistently outperforms strong baseline models, yielding statistically significant improvements and reduced cross-domain variance. These findings demonstrate that noncommutative algebraic dynamics can serve as a practical and reproducible foundation for machine creativity. Notably, this architecture has already been deployed in real-world enterprise environments.