Integrating Transformer-Based Semantic Embeddings with Quantum Probability for Multidimensional Real Estate Valuation

Abstract

Traditional real estate valuation methods predominantly emphasize quantitative financial metrics, often overlooking qualitative factors that influence stakeholder perceptions and decisionmaking. This work proposes an integrative framework combining transformer-based Large Language Models for semantic extraction of textual property descriptors with Quantum Probability Theory to model valuation as quantum states within a complex Hilbert space. Such an approach captures the superposition of qualitative attributes and their interference effects, reflecting the diverse and sometimes conflicting perspectives of stakeholders. Non-commutative operator sequences capture the order-dependent nature of evaluations, while unitary transformations encode alignment and conflict across valuation criteria. By embedding narrative-rich qualitative data into multidimensional quantum state vectors, this methodology enables a nuanced representation of property value that transcends additive classical models. The framework addresses limitations of conventional income-based and market comparison approaches by incorporating intangible dimensions such as cultural heritage, environmental impact, and social value into formal probabilistic computations. This synthesis offers a pathway to more comprehensive, context-sensitive property appraisals that accommodate stakeholder diversity and dynamic valuation contexts through mathematically rigorous yet flexible structures.