# QuantumQUBO Agent: Automating Quadratic Unconstrained Binary Optimization (QUBO) Formulation Generation from Natural Language

arXiv: https://arxiv.org/abs/2609.10629 · HTML: https://mlsanity.com/paper/2609.10629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://mlsanity.com/paper/2504.16918/) (2025)
- [Feature Selection on Quantum Computers](https://mlsanity.com/paper/2203.13261/) (2022)
- [Q-Seg: Quantum Annealing-Based Unsupervised Image Segmentation](https://mlsanity.com/paper/2311.12912/) (2023)
- [LLM-QUBO: An End-to-End Framework for Automated QUBO Transformation from Natural Language Problem Descriptions](https://mlsanity.com/paper/2509.00099/) (2025)
- [Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing](https://mlsanity.com/paper/2307.06542/) (2023)
- [Quantum Annealing for Computer Vision Minimization Problems](https://mlsanity.com/paper/2312.12848/) (2023)
- [Decomposed Quadratization: Efficient QUBO Formulation for Learning Bayesian Network](https://mlsanity.com/paper/2006.06926/) (2020)
- [Cyber Risk Scoring with QUBO: A Quantum and Hybrid Benchmark Study](https://mlsanity.com/paper/2512.18305/) (2025)

## Abstract (arXiv)

Quadratic Unconstrained Binary Optimization (QUBO) is a central formulation for combinatorial optimization and has gained increasing attention due to its compatibility with quantum, hybrid quantum-classical, and quantum-inspired solvers. However, translating natural-language problem descriptions into correct QUBO formulations remains difficult, requiring the identification of binary variables, constraints, objective functions, penalty terms, and suitable penalty weights. This process is time-consuming and often demands substantial domain expertise. To address this challenge, we propose an end-to-end multi-agent framework that automatically generates QUBO formulations from natural-language problem descriptions, supported by structured or unstructured test cases. To evaluate its performance, We also introduce QUBOBench, a benchmark containing 100 combinatorial optimization problems across 12 application domains, curated from peer-reviewed literature, competitions, and canonical NP-hard problems. Experimental results show that our framework achieves 68% accuracy on QUBOBench, outperforming a direct single-call baseline by 22%. Further analysis identifies iterative self-repair as the most important component contributing to improved performance. The data and code are open-sourced at https://quitttcat.github.io/QuantumQUBOAgent.