Extending Ontologies: From Dense Embeddings to Hybrid Quantum-Fuzzy Systems

This paper presents a versatile framework for evaluating fuzzy quantification queries over both standard and fuzzy ontologies as well as knowledge graphs. The primary objective is the retrieval of individuals that satisfy queries articulated via Type I or Type II fuzzy quantified expressions. A key advantage of the proposed approach is its inherent adaptability: it remains entirely agnostic to the quantifier type, the underlying evaluation method, and the specific data source of the ontology (i.e., OWL ontologies or RDFS knowledge graphs). Furthermore, we present Q2S2, a publicly accessible implementation of this system developed to support future research.

An advanced retrieval-augmented generation pipeline is typically assembled from three or four independently operated systems: an approximate nearest-neighbour index, a full-text search engine, a graph database, and a relational document store. Each contributes its own deployment surface, configuration model, and failure modes, and the integration logic that binds them is written anew in every project. In this work, we present \textsc{Quanta}, an open-source Python library, which unifies dense vector search over 4-bit quantised embeddings, BM25 full-text retrieval, and knowledge-graph traversal behind a single retrieval API. Quanta makes two design commitments, which distinguish it from existing hybrid retrieval stacks. First, signals are combined by \emph{weighted reciprocal rank fusion} rather than by normalising heterogeneous scores onto a shared range, which we argue is ill-posed because such normalisations are query-dependent. Second, the graph is a \emph{candidate expander and not a relevance scorer}: traversal widens the candidate pool, and the newly admitted documents are re-scored by the dense indexes under an identifier allowlist, so structural adjacency determines what is considered while content evidence determines how it ranks.

Large language models (LLMs) exhibit abilities beyond natural language modelling and text generation. Recent advances in their reasoning capabilities have spurred interest in applying LLMs to complex scientific tasks requiring deep domain expertise and sophisticated reasoning. Quantum computing, as a highly specialised field with significant knowledge barriers and hardware constraints, could greatly benefit from such advancements. However, a key open question that first must be answered is: How can we develop fine-tuning pipelines that instil genuine quantum reasoning in LLMs, rather than task-specific pattern matching? We study this question through quantum circuit simulation as a training objective, where the model must predict the measurement probability distribution resulting from a sequence of quantum gate operations. We propose and compare two fine-tuning pipelines: (1) Supervised Fine-Tuning (SFT) on explicit gate-by-gate state-vector simulation traces, and (2) a two-stage SFT+Group Relative Policy Optimisation (GRPO) approach that sequentially applies SFT followed by GRPO with verifiable rewards. Our findings show that SFT achieves near-perfect in-distribution and gate-count extrapolation accuracy, significantly outperforming both the base model and the GPT-OSS-120B baseline. SFT+GRPO trades some in-distribution precision for better generalisation to larger qubit systems that SFT alone cannot handle. Both pipelines significantly outperform the baselines, demonstrating that targeted fine-tuning on explicit reasoning traces is an effective strategy for advancing quantum reasoning in LLMs.