# LLM-QUBO: An End-to-End Framework for Automated QUBO Transformation from Natural Language Problem Descriptions

arXiv: https://arxiv.org/abs/2509.00099 · HTML: https://mlsanity.com/paper/2509.00099/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [Penalty Weights in QUBO Formulations: Permutation Problems](https://mlsanity.com/paper/2206.11040/) (2022)
- [End-to-End Portfolio Optimization with Quantum Annealing](https://mlsanity.com/paper/2504.08843/) (2025)

## Built on by (most cited first, 3 of 3)

- [Quantum-Inspired Trace-Augmented Evidence Selection for Reasoning over Structured Hypothesis Spaces](https://mlsanity.com/paper/2606.06941/) (2026)
- [Leveraging LLM-Based Agentic Systems to Generate Quantum Applications for Test Optimization](https://mlsanity.com/paper/2607.00939/) (2026)
- [QuantumQUBO Agent: Automating Quadratic Unconstrained Binary Optimization (QUBO) Formulation Generation from Natural Language](https://mlsanity.com/paper/2609.10629/) (2026)

## Abstract (arXiv)

Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions into the requisite Quadratic Unconstrained Binary Optimization (QUBO) format and the scalability limitations of current quantum hardware. To address these obstacles, we propose a novel end-to-end framework, LLM-QUBO, that automates this entire formulation-to-solution pipeline. Our system leverages a Large Language Model (LLM) to parse natural language, automatically generating a structured mathematical representation. To overcome hardware limitations, we integrate a hybrid quantum-classical Benders' decomposition method. This approach partitions the problem, compiling the combinatorial complex master problem into a compact QUBO format, while delegating linearly structured sub-problems to classical solvers. The correctness of the generated QUBO and the scalability of the hybrid approach are validated using classical solvers, establishing a robust performance baseline and demonstrating the framework's readiness for quantum hardware. Our primary contribution is a synergistic computing paradigm that bridges classical AI and quantum computing, addressing key challenges in the practical application of optimization problem. This automated workflow significantly reduces the barrier to entry, providing a viable pathway to transform quantum devices into accessible accelerators for large-scale, real-world optimization challenges.