This paper presents a general method to derive automatically a Quadratic Unconstrained Binary Optimisation (QUBO) formulation of, in principle, any combinatorial optimisation problem from its high-level description given in any programming language in a free format. Currently ad-hoc approaches to formulating a problem at a time as a QUBO are the norm. The proposed method goes beyond the state-of-the-art as it is general in its applicability. The method is data-driven and based on sampling, but the obtained QUBO is exact rather than only an approximation of the original problem for optimisation problems occurring in practice. The method is of particular interest in the context of Quantum Ising Machines - quantum computers specialised to optimisation tasks. It can be understood as a compiler that makes these machines usable without specific expertise by automating the translation of high-level description of combinatorial optimisation problems to a low-level format suitable for the quantum hardware.
This paper presents a general method to derive automatically a Quadratic Unconstrained Binary Optimisation (QUBO) formulation of, in principle, any combinatorial optimisation problem from its high-level description given in any programming language in a free format. Currently ad-hoc approaches to formulating a problem at a time as a QUBO are the norm. The proposed method goes beyond the state-of-the-art as it is general in its applicability. The method is data-driven and based on sampling, but the obtained QUBO is exact rather than only an approximation of the original problem for optimisation problems occurring in practice. The method is of particular interest in the context of Quantum Ising Machines - quantum computers specialised to optimisation tasks. It can be understood as a compiler that makes these machines usable without specific expertise by automating the translation of high-level description of combinatorial optimisation problems to a low-level format suitable for the quantum hardware.
The QUBO framework provides a way to model, in principle, any combinatorial optimization problem and enables the use of Ising machines to solve it. Ising machines are devices designed to quickly find good solutions to QUBO problems. In previous work, Auto-QUBO was designed to automatically generate QUBO formulations from a high-level problem description. We address two shortcomings of this method. It only works on a per-instance basis, making repeated formulations for similar problems inefficient, and relies on the user to specify penalty weights. This work introduces symbolic sampling, which provides QUBO formulations for entire problem classes. We demonstrate the speedup that can be achieved with this approach using instances of the maximum clique problem. Additionally, we use proven methods to compute valid penalty weights automatically to simplify the translation process. By providing a user-friendly way to generate QUBO formulations in an efficient manner, both in terms of time and problem difficulty, we enable more people to use Ising machines for combinatorial optimization.
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.
Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains challenging and currently requires problem-specific analytical derivations. Moreover, such explicit formulations impose tangible constraints on solution encodings. In stark contrast to prior work, this paper proposes to learn QUBO forms from data through gradient backpropagation instead of deriving them. As a result, the solution encodings can be chosen flexibly and compactly. Furthermore, our methodology is general and virtually independent of the specifics of the target problem type. We demonstrate the advantages of learnt QUBOs on the diverse problem types of graph matching, 2D point cloud alignment and 3D rotation estimation. Our results are competitive with the previous quantum state of the art while requiring much fewer logical and physical qubits, enabling our method to scale to larger problems. The code and the new dataset will be open-sourced.
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.
We present PyQUBO, an open-source Python library for constructing quadratic unconstrained binary optimizations (QUBOs) from the objective functions and the constraints of optimization problems. PyQUBO enables users to prepare QUBOs or Ising models for various combinatorial optimization problems with ease thanks to the abstraction of expressions and the extensibility of the program. QUBOs and Ising models formulated using PyQUBO are solvable by Ising machines, including quantum annealing machines. We introduce the features of PyQUBO with applications in the number partitioning problem, knapsack problem, graph coloring problem, and integer factorization using a binary multiplier. Moreover, we demonstrate how PyQUBO can be applied to production-scale problems through integration with quantum annealing machines. Through its flexibility and ease of use, PyQUBO has the potential to make quantum annealing a more practical tool among researchers.
Optimizing objective functions stands to benefit significantly from leveraging quantum computers, promising enhanced solution quality across various application domains in the future. However, harnessing the potential of quantum solvers necessitates formulating problems according to the Quadratic Unconstrained Binary Optimization (QUBO) model, demanding significant expertise in quantum computation and QUBO formulations. This expertise barrier limits access to quantum solutions. Fortunately, automating the conversion of conventional optimization problems into QUBO formulations presents a solution for promoting accessibility to quantum solvers. This article addresses the unmet need for a comprehensive automatic framework to assist users in utilizing quantum solvers for optimization tasks while preserving interfaces that closely resemble conventional optimization practices. The framework prompts users to specify variables, optimization criteria, as well as validity constraints and, afterwards, allows them to choose the desired solver. Subsequently, it automatically transforms the problem description into a format compatible with the chosen solver and provides the resulting solution. Additionally, the framework offers instruments for analyzing solution validity and quality. Comparative analysis against existing libraries and tools in the literature highlights the comprehensive nature of the proposed framework. Two use cases (the knapsack problem and linear regression) are considered to show the completeness and efficiency of the framework in real-world applications. Finally, the proposed framework represents a significant advancement towards automating quantum computing solutions and widening access to quantum optimization for a broader range of users. The framework is publicly available on GitHub (https://github.com/cda-tum/mqt-qao) as part of the Munich Quantum Toolkit (MQT).