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.

翻译：大型语言模型（LLM）在生成流畅且语境适宜的文本方面取得了显著成功；然而，其产生真正创造性输出的能力仍然有限。本文认为，这种局限性源于当代LLM的一种结构特性：当提供丰富语境时，未来生成的空间会受到强烈约束，且生成过程实际上由近乎确定性的动力学所支配。诸如测试时缩放和语境适应等近期方法虽然提升了性能，但并未从根本上改变这一约束。为解决此问题，我们提出代数量子智能（AQI）作为一种计算框架，能够实现语义空间的系统性扩展。AQI被构建为一种受量子理论启发的非交换代数结构，允许以可控且可设计的方式实现顺序依赖性、干涉和不确定性等特性。语义态被表示为希尔伯特空间中的向量，其演化由非交换算子计算出的C值所支配，从而确保多种未来语义可能性的共存与扩展。在本研究中，我们通过扩展一个基于Transformer的LLM，引入超过600个专用算子来实现AQI。我们在LLM作为评判者的协议下，在涵盖十个领域的创造性推理基准上评估了所得系统。结果表明，AQI持续优于强基线模型，产生了统计上显著的改进并降低了跨领域方差。这些发现证明，非交换代数动力学可作为机器创造力的一种实用且可复现的基础。值得注意的是，该架构已在真实的企业环境中部署。