# Quantum-Inspired Trace-Augmented Evidence Selection for Reasoning over Structured Hypothesis Spaces

arXiv: https://arxiv.org/abs/2606.06941 · HTML: https://mlsanity.com/paper/2606.06941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Synchromesh: Reliable code generation from pre-trained language models](https://mlsanity.com/paper/2201.11227/) (2022)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Efficient Benchmarking of Language Models](https://mlsanity.com/paper/2308.11696/) (2023)
- [SparseMAP: Differentiable Sparse Structured Inference](https://mlsanity.com/paper/1802.04223/) (2018)
- [Rethinking Mixture-of-Agents: Is Mixing Different Large Language Models Beneficial?](https://mlsanity.com/paper/2502.00674/) (2025)
- [LEXam: Benchmarking Legal Reasoning on 340 Law Exams](https://mlsanity.com/paper/2505.12864/) (2025)
- [Towards Reasoning Ability of Small Language Models](https://mlsanity.com/paper/2502.11569/) (2025)
- [Ensemble Learning for Large Language Models in Text and Code Generation: A Survey](https://mlsanity.com/paper/2503.13505/) (2025)
- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)
- [Quantum Natural Language Processing: A Comprehensive Review of Models, Methods, and Applications](https://mlsanity.com/paper/2504.09909/) (2025)
- [Bench360: Benchmarking Local LLM Inference from 360 Degrees](https://mlsanity.com/paper/2511.16682/) (2025)
- [LLM-QUBO: An End-to-End Framework for Automated QUBO Transformation from Natural Language Problem Descriptions](https://mlsanity.com/paper/2509.00099/) (2025)
- [On Quadratization of Pseudo-Boolean Functions](https://mlsanity.com/paper/1404.6538/) (2014)
- [Combinatorial Reasoning: Selecting Reasons in Generative AI Pipelines via Combinatorial Optimization](https://mlsanity.com/paper/2407.00071/) (2024)
- [Quantum Annealing for Machine Learning: Applications in Feature Selection, Instance Selection, and Clustering](https://mlsanity.com/paper/2507.15063/) (2025)

## Abstract (arXiv)

Large language models (LLMs) now solve a wide range of expert-level exams at or above human level, yet remain brittle on specialised, evidence-intensive domains such as law. On these tasks, errors arise not only from gaps in world knowledge but also from subtle distinctions between pieces of evidence and inconsistent use of supporting evidence. The most common aggregator over sampled chain-of-thought (CoT) traces, majority vote, returns the most popular answer regardless of whether its evidence is actually strongest. We propose to treat the selection of CoT reasoning fragments into a set of evidence as an explicit combinatorial optimisation problem, allowing well-supported but minority hypotheses to override noisy majorities, and to evaluate the approach on legal-reasoning benchmarks that are particularly sensitive to evidence quality. We introduce EP-HUBO (Evidence Pool Higher-Order Binary Optimisation), which generates multiple CoT traces with a small local model, parses fragments into per-hypothesis evidence pools, solves a higher-order unconstrained binary optimisation per pool with quality-derived weights (relevance, specificity, distinctiveness), and delegates a single adjudication call per question to a frontier model. We evaluate EP-HUBO on two evidence-intensive legal benchmarks using both simulated annealing on classical hardware and the Dirac-3 photonic entropy-quantum machine from Quantum Computing Inc. HUBO-style optimisation gives a principled way to aggregate reasoning fragments while preserving minority-but-correct hypotheses, and is most valuable in low-contamination domains where frontier models have not already absorbed the benchmark material.