As quantum computing emerges as a powerful tool for solving combinatorial optimization problems, the absence of intuitive programming interfaces remains a major barrier to practical adoption. This work presents a secure and resilient natural language interface that translates high-level optimization prompts into QUBO (Quadratic Unconstrained Binary Optimization) formulations suitable for quantum solvers such as D-Wave. The translation pipeline leverages large language models (LLMs) and incorporates multiple verification layers, including schema validation, constraint compliance checks, and reverse translation for semantic fidelity auditing. Fidelity is quantified using cosine similarity between sentence embeddings of the original and reconstructed problem descriptions, enabling intent alignment analysis. We evaluate the system across 100 optimization instances spanning five canonical problem types: Knapsack, Traveling Salesman Problem, Graph Coloring, Seating Assignment, and Team Assignment. Results show that GPT-4 significantly outperforms GPT-3.5 in complex cases such as TSP, achieving up to$90\%$success rates where earlier models fail entirely. Latency measurements confirm interactive performance, with most translations completing in under 6 seconds. These results demonstrate the feasibility of trustworthy natural language interfaces for quantum optimization and provide a framework for verifiable, interpretable, and efficient translation from user intent to quantum-executable code.
As quantum computing emerges as a powerful tool for solving combinatorial optimization problems, the absence of intuitive programming interfaces remains a major barrier to practical adoption. This work presents a secure and resilient natural language interface that translates high-level optimization prompts into QUBO (Quadratic Unconstrained Binary Optimization) formulations suitable for quantum solvers such as D-Wave. The translation pipeline leverages large language models (LLMs) and incorporates multiple verification layers, including schema validation, constraint compliance checks, and reverse translation for semantic fidelity auditing. Fidelity is quantified using cosine similarity between sentence embeddings of the original and reconstructed problem descriptions, enabling intent alignment analysis. We evaluate the system across 100 optimization instances spanning five canonical problem types: Knapsack, Traveling Salesman Problem, Graph Coloring, Seating Assignment, and Team Assignment. Results show that GPT-4 significantly outperforms GPT-3.5 in complex cases such as TSP, achieving up to90%success rates where earlier models fail entirely. Latency measurements confirm interactive performance, with most translations completing in under 6 seconds. These results demonstrate the feasibility of trustworthy natural language interfaces for quantum optimization and provide a framework for verifiable, interpretable, and efficient translation from user intent to quantum-executable code.
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.
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.
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).
Large language models have recently shown potential in bridging the gap between classical machine learning and quantum machine learning. However, the lack of standardized, high-quality datasets and robust translation frameworks limits progress in this domain. We introduce Q-Bridge, an LLM-guided code translation framework that systematically converts CML implementations into executable QML variants. Our approach builds on a self-involving pipeline that iteratively expands a verified seed codebase into a large-scale dataset, CML-2-QML, integrating verifiable and unverifiable code pairs. The Q-Bridge model is fine-tuned using supervised LoRA adaptation for scalable and memory-efficient training, achieving faithful and interpretable quantum code generation across diverse architectures. Empirical analysis confirms the feasibility of direct CML-to-QML translation and reveals consistent structural alignment between classical and quantum paradigms. Case studies further demonstrate that Q-Bridge can maintain deterministic correctness and also enable creative architectural exploration. This work establishes the first reproducible framework and dataset for LLM-driven quantum code translation, offering a foundation for scalable quantum AI development.
Abstract As interest in quantum and related optimization paradigms continues to grow, fairly and systematically comparing their performance across practical problem settings remains challenging. This challenge arises because these approaches often target different problem classes, use different mathematical representations, and are affected differently by modeling choices. As a result, observed performance depends not only on the solver itself, but also on how a problem is formulated, reformulated, and translated into a solver-specific input language. This work presents a publicly available and extensible benchmarking framework that unifies advances in quantum, quantum-hybrid, quantum-inspired, and classical optimization by enabling consistent comparison across use cases, solvers, and models. We address the diversity of solver “languages”—from mixed-integer programming (MIP) formulations for branch-and-bound methods over quadratic unconstrained binary optimization (QUBO) models for quantum annealers to constrained quadratic models (CQM) for hybrid approaches — as well as the influence of modeling choices, such as binary encodings and penalty formulations, on both performance and solution fidelity. By supporting systematic variation across the three dimensions of use case, solver, and model, the framework reveals trade-offs that single-dimension benchmarks overlook, clarifies when native formulations are preferable, and enables rigorous evaluation of practical combinatorial optimization problems. The two case studies, vehicle routing and maximum cut, illustrate this principle: their contrasting outcomes show that the effectiveness of a solver depends strongly on how well the chosen model representation matches the solver backend and the use case.
Alignment-based conformance checking is a central task in process mining, but computing optimal alignments is computationally hard. This paper studies whether the alignment problem can be expressed directly as a Quadratic Unconstrained Binary Optimization problem and explored with quantum annealing. We present a direct QUBO formulation for optimal alignments on safe Petri nets, with a proof-of-concept implementation supporting exact solving, simulated annealing, and a D-Wave Advantage2 quantum processing unit. The study is intentionally preliminary: rather than claiming a practical quantum advantage, we test whether the formulation is semantically correct and where current hardware helps or fails. On small representative benchmarks, the QUBO recovers correct optimal alignments, including concurrency, loops, silent transitions, and duplicate labels. On loop-heavy instances, the quantum annealer can outperform simulated annealing on success probability. Scalability, however, is strongly limited by hardware connectivity and embedding overhead. Overall, direct QUBO-based alignment finding is feasible in principle, but still far from practical large-scale use.