QUBO-Optimized Evidence Selection for Retrieval-Augmented Question Answering with Unconventional Solvers

Retrieval-augmented question answering depends on selecting evidence passages that jointly support answer generation. However, many RAG pipelines rely on top-(k) ranking, where passages are selected mainly by individual relevance scores, even though multi-hop questions often require complementary evidence satisfying multiple information requirements. Recent LLM-based selectors address this by treating retrieval as set selection, but using an LLM for this intermediate stage can be costly and difficult to scale. In this work, we formulate evidence selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Given a question, candidate passages, and decomposed information requirements, our method constructs an energy function that balances relevance, requirement coverage, support strength, redundancy, complementarity, and compactness. Low-energy solutions correspond to compact evidence subsets that cover the needed requirements while avoiding unnecessary or repetitive context. The selected passages are then passed to a downstream language model for answer generation, separating combinatorial evidence selection from semantic answer generation. We evaluate the proposed QUBO selector on HotpotQA and compare it with LLM-based set selectors and non-LLM baselines including BM25, relevance top-(k), maximal marginal relevance, hybrid lexical--semantic ranking, greedy coverage, and random selection. The QUBO selector achieves competitive exact-match and token-F1 performance relative to LLM-based selectors while providing a solver-compatible formulation for structured evidence selection. These results suggest that multi-hop evidence selection can be cast as discrete optimization, opening a path toward RAG pipelines where LLMs are reserved for semantic processing and answer generation, while context selection is handled by Ising/QUBO-compatible solvers.