# Algebraic Quantum Intelligence: A New Framework for Reproducible Machine Creativity

arXiv: https://arxiv.org/abs/2602.14130 · HTML: https://mlsanity.com/paper/2602.14130/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 15 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memory](https://mlsanity.com/paper/2509.25140/) (2025)
- [AgentEvolver: Towards Efficient Self-Evolving Agent System](https://mlsanity.com/paper/2511.10395/) (2025)
- [Thought calibration: Efficient and confident test-time scaling](https://mlsanity.com/paper/2505.18404/) (2025)
- [The Art of Scaling Test-Time Compute for Large Language Models](https://mlsanity.com/paper/2512.02008/) (2025)
- [A Survey of Quantum Theory Inspired Approaches to Information Retrieval](https://mlsanity.com/paper/2007.04357/) (2020)
- [Creative Problem Solving in Large Language and Vision Models -- What Would it Take?](https://mlsanity.com/paper/2405.01453/) (2024)
- [Semantic Hilbert Space for Text Representation Learning](https://mlsanity.com/paper/1902.09802/) (2019)
- [Quantum-Like Contextuality in Large Language Models](https://mlsanity.com/paper/2412.16806/) (2024)

## Abstract (arXiv)

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.