Quantum Semantic Dynamics: A Unified Framework for N-Dimensional Semantic Hilbert Spaces with Experimental Validation

Keywords: quantum, semantics, distributional semantic models, large language models, agents

TL;DR: We extended quantum semantic theory to N-dimensional Hilbert spaces, demonstrated Bell inequality violations in semantic systems, and successfully implemented the framework in the quantum computing toolkit Qiskit.

Abstract:

Natural language ambiguity and context-dependence challenge classical computational models. We present a mathematical framework extending quantum semantics to N-dimensional Hilbert spaces, integrating semantic spaces, dynamic Hamiltonians, quantum field theory, decoherence modeling, and computational implementation. We demonstrate Bell inequality violations (CHSH = 2.4$\pm$0.1) providing experimental validation of quantum-like semantic behavior. Our framework achieves quantized semantic energy spectra with Wigner-Dyson statistics, semantic entanglement with concurrence values ranging from $0.75$ to $0.9$, and decoherence timescales of 20-100 operations that align with empirical context stability in human language processing. These results
establish a blueprint for implementing and testing this framework on quantum
computers to determine whether semantic representations can be realized as
genuine quantum states for natural language understanding.

Submission Number: 314