Quantum-Natural-Language Semantics

Functorial grammar and vector/tensor meanings used in categorical and quantum-inspired NLP. The main concepts are pregroup grammar, compositional circuits, evaluation. Each must be defined in the context of a concrete physical model, mathematical representation, or experimental task. Terminology alone does not establish the behavior of the system.

Categorical compositional semantics maps grammatical reductions into tensor contractions or diagrams that combine word meanings. A quantum language circuit is meaningful only when the grammar, tensor encoding, optimization objective and downstream linguistic task are specified. High-dimensional Hilbert-space notation alone does not establish semantic adequacy or a learning advantage over classical compositional models.

Construct a small typed grammar and compute both a classical tensor-network contraction and its corresponding quantum-circuit observable. Evaluate on held-out grammatical contrasts and explicit semantic labels, with controlled vocabulary and measurement-shot budgets. Test sensitivity to lexical ambiguity and sentence length rather than comparing only training-set losses.