Algebraic Quantum Intelligence: A New Framework for Reproducible Machine Creativity

TL;DR

The results show that AQI consistently outperforms strong baseline models, yielding statistically significant improvements and reduced cross-domain variance, and demonstrate that noncommutative algebraic dynamics can serve as a practical and reproducible foundation for machine creativity.

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.

Figures (6)

• Figure 1: Conceptual semantic branching of non-commutative semantic dynamics in Algebraic Quantum Intelligence (AQI). While conventional LLMs exhibit convergence toward a single semantic trajectory as contextual constraints increase, AQI maintains multiple future semantic possibilities through non-commutative operator interactions, preventing premature collapse of exploration.
• Figure 2: Algebraic Quantum System (AQS) as a generalization framework encompassing Physical Quantum Systems (PQS). AQS abstracts the minimal algebraic structures---state space, non-commutative operators, inner products, and generator-based dynamics---required to produce order dependence, interference, and uncertainty, without imposing physical constraints such as unitarity or measurement postulates.
• Figure 3: Two-layer architecture of AQI: alternating state update and operator update. The semantic state $\lvert \psi_k \rangle$ is updated by a dynamically generated creative Hamiltonian H(k) (S-Generator), while the Hamiltonian itself is adaptively constructed based on the current state and prior dynamics (H-Generator), enabling non-commutative semantic evolution across message units.
• Figure 4: Performance comparison across ten creative reasoning domains measured by the Co-Creativity Index (CCI). AQI consistently outperforms 14 strong baseline models, showing an average improvement of +27 T-score points while exhibiting reduced variance across domains, indicating both higher creativity and greater stability.
• Figure 5: Order-dependent semantic divergence induced by non-commutative operators. Embedding projections (PCA) of outputs generated under two conditions---$A\to B$ (Super CFO $\to$ Super CHRO) and $B\to A$---form clearly separated clusters even at temperature = 0, demonstrating systematic trajectory bifurcation driven solely by operator order.