Quantum optimization has become one of the central areas in the search for practical quantum advantage. The field has developed rapidly, with substantial progress in QAOA and its variants, other variational quantum algorithms, hybrid quantum-classical workflows, and early hardware demonstrations. At the same time, the path toward scalable and practically useful quantum optimization remains uncertain. Current approaches are dominated by a small number of modeling and algorithmic templates, most notably QUBO mappings and QAOA-type algorithms. These have provided a valuable common foundation, but it is not clear if they will be sufficient for the diversity, scale, and structure of optimization problems encountered in realistic applications.

The purpose of this Dagstuhl Seminar is to bring together researchers already active in quantum computing, quantum algorithms, combinatorial optimization, mathematical programming, operations research, high-performance computing, and application-driven optimization to address this gap. The central question is how to move from proof-of-concept quantum optimization toward scalable, structure-aware, hardware-conscious methods that can be meaningfully compared with state-of-the-art classical and hybrid approaches. We aim to create a focused forum for researchers who understand both the promise and the limitations of current quantum optimization techniques and who are interested in developing the next generation of methods.

A major theme will be the design of hybrid quantum-classical optimization algorithms that go beyond the standard templates. We will discuss how quantum subroutines can be embedded into scalable classical optimization workflows, including decomposition methods, relaxation and rounding schemes, branch-and-bound or branch-and-cut frameworks, local improvement, sampling-based heuristics, multilevel methods, and HPC/GPU-assisted pipelines. Relevant questions include but are not limited to how to select and formulate quantum subproblems, how to train parameters at scale and how to use classical preprocessing and postprocessing effectively, and vice versa: how to use quantum methods to facilitate the classical ones. A second theme will be modeling, encoding, and constraint handling. Many practically relevant optimization problems are not naturally unconstrained, and reducing them to QUBO often destroys the structure. We will discuss compact encodings, constraint-preserving mixers, non-penalty formulations, and other methods focusing on scalability. A third focus will be algorithmic diversity beyond QAOA. The seminar will consider QAOA and its generalizations, but also alternative paradigms. We are particularly interested in identifying reusable algorithmic primitives for optimization and understanding how these primitives interact with problem structure, hardware constraints, and classical optimization layers. We will also discuss multi-solution, distributional, and multi-objective optimization problems, where the desired output is not necessarily a single optimal bit string but a set of high-quality solutions, an approximation of a Pareto front, a robust or fair solution set, or a useful probability distribution over feasible or near-optimal configurations as such problems may be especially natural for quantum computing.

The seminar will be organized around such research questions as: Which problem classes and encodings offer credible opportunities for quantum or hybrid advantage? What are the right notions of scalability for quantum optimization? How can ideas from classical optimization theory, decomposition, and large-scale computation inform ansatz design, mixer construction, and parameter strategies? How should benchmarks be designed so that they reflect realistic structure rather than only small synthetic QUBO instances? What role should AI and learning methods play in quantum optimization? How to design scalable quantum algorithms?

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Stephan Eidenbenz, Thorsten Koch, Ilya Safro, and Stefan Woerner

This seminar qualifies for Dagstuhl's LZI Junior Researchers program. Schloss Dagstuhl wishes to enable the participation of junior scientists with a specialisation fitting for this Dagstuhl Seminar, even if they are not on the radar of the organizers. Applications by outstanding junior scientists are possible until Friday, August 21, 2026.