arXiv subjects

Hausi Müller

Publications and source records attributed to Hausi Müller.

6 recordsLinked to original sources

arXiv2026

Qubit-efficient and gate-efficient encodings of graph partitioning problems for quantum optimization

We introduce a qubit- and gate-efficient higher-order unconstrained binary optimization (HUBO) encoding for graph partitioning problems requiring label-count minimization. This widely applicable class of problems includes minimum graph coloring, minimum \textit{k}-cut, and community detection. To the best of our knowledge, this is the first work to address the optimization versions of these problems in a quantum setting, rather than only their decision counterparts. Our construction encodes each vertex variable in a number of bits logarithmic in the number of available labels---the information-theoretic minimum---and employs a novel lexicographic penalty system that implicitly minimizes partition count without requiring dedicated indicator variables. We derive provably sufficient conditions on all penalty coefficients, including those arising from Rosenberg quadratization, guaranteeing feasibility and optimality of the lowest-energy solution. Analogous conditions are derived for a one-hot encoding to enable controlled comparison. We also show that our encoding reduces two-qubit gate count per layer of the quantum approximate optimization algorithm (QAOA). Benchmarking on a quantum annealer demonstrates that our logarithmic encoding greatly improves solution quality and time-to-solution for minimum graph coloring relative to one-hot encoding, with greater advantage as problem size increases.

quant-ph↗

arXiv2026

Experimental Workflows for Combinatorial Optimization: Towards Quantum Advantage

Demonstrating quantum advantage for combinatorial optimization requires more than standalone algorithmic results; it calls for end-to-end case studies that integrate problem modelling, quantum execution, and classical refinement into practical workflows. This paper presents a sandbox platform for experimenting with hybrid quantum-classical workflows in graph optimization, enabling the systematic study of end-to-end optimization pipelines. Using our platform, we investigate three classically intractable and mutually reducible graph problems -- Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique -- by transforming them into an unconstrained problem and solving the resulting instances with QAOA on IBM platforms. Our workflow combines classical pre-processing to reduce instance size, quantum optimization on the reduced problem, and classical postprocessing to map quantum outputs to high-quality feasible solutions, thereby avoiding direct constraint encoding in the quantum circuit. We evaluate the approach on synthetic graphs, benchmark instances, and real-world networks, and report hardware experiments on IBM Quantum System One at PINQ2 in Bromont, Quebec, powered by IBM's 156-qubit Heron r2 processor on graphs up to 128 vertices, with circuits involving up to 128 qubits and 13,555 two-qubit gates. The results illustrate how sandbox-style end-to-end experimentation can expose bottlenecks, clarify the role of classical-quantum workload partitioning, and provide domain experts and practitioners with a practical guide for interpreting quantum optimization outputs and assessing quantum utility on the road to quantum advantage in combinatorial optimization.

quant-ph↗

arXiv2025

SCOOP: A Quantum-Computing Framework for Constrained Combinatorial Optimization

While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal solutions. The Quantum Approximate Optimization Algorithm (QAOA) is a state-of-the-art hybrid quantum-classical approach for tackling these challenging problems that are encoded using quadratic and higher-order unconstrained binary optimization problems (QUBO and HUBO). We present SCOOP, a novel QAOA-based framework for solving constrained optimization problems. SCOOP transforms a constrained problem into an unconstrained counterpart, forming SCOOP problem twins. The QAOA quantum algorithm operates on the unconstrained twin to identify potential optimal and near-optimal solutions. Effective classical post-processing reduces the solution set to the constrained problem space. Our SCOOP approach is solution-enhanced, objective-function-compatible, and scalable. We demonstrate the framework on three NP-hard problems, Minimum Dominating Set, Minimum Maximal Matching, and Minimum Set Cover appearing in practical application domains such as resource allocation, communication networks, and machine learning. We validate SCOOP's feasibility and effectiveness on Xanadu PennyLane simulators.

quant-ph↗

arXiv2025

The Art of Avoiding Constraints: A Penalty-free Approach to Constrained Combinatorial Optimization with QAOA

The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model unconstrained combinatorial optimization problems. While the solution space of an unconstrained combinatorial optimization problem consists of all possible combinations of the objective function's decision variables, for a constrained combinatorial optimization problem, the solution space consists only of solutions that satisfy the problem constraints. While solving such a QUBO problem optimally results in an optimal solution to the underlying constrained problem, setting the right penalty parameters is crucial. Moreover, finding suitable penalties that ensure near-optimal solutions is also challenging. In this article, we introduce our innovative profit-relaxation framework to solve constrained combinatorial optimization problems. Our effective hybrid approach transforms a selected constrained combinatorial optimization problem into an unconstrained profit problem, such that the solution spaces of the two problems are interrelated with respect to their solution qualities. This allows us to determine optimal and near-optimal solutions for the constrained problem. We use three NP-hard problems -- Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique -- to demonstrate the feasibility and effectiveness of our approach. We conducted a detailed performance evaluation of our profit-relaxation framework on two different platforms: Xanadu PennyLane and Argonne QTensor Quantum Circuit Simulator.

quant-ph↗

arXiv2022

A QUBO model of the RNA folding problem optimized by variational hybrid quantum annealing

RNAs self-interact through hydrogen-bond base-pairing between nucleotides and fold into specific, stable structures that substantially govern their biochemical behaviour. Experimental characterization of these structures remains difficult, hence the desire to predict them computationally from sequence information. However, correctly predicting even the base pairs involved in the folded structure of an RNA, known as secondary structure, from its sequence using minimum free energy models is understood to be NP-hard. Classical approaches rely on heuristics or avoid considering pseudoknots in order to render this problem more tractable, with the cost of inexactness or excluding an entire class of important RNA structures. Given their prospective and demonstrable advantages in certain domains, including combinatorial optimization, quantum computing approaches by contrast have the potential to compute the full RNA folding problem while remaining more feasible and exact. Herein, we present a physically-motivated QUBO model of the RNA folding problem amenable to both quantum annealers and circuit-model quantum computers and compare the performance of this formulation versus current RNA folding QUBOs after tuning the parameters of all against known RNA structures using an approach we call "variational hybrid quantum annealing".

quant-ph↗

arXiv2015

Using Models at Runtime to Address Assurance for Self-Adaptive Systems

A self-adaptive software system modifies its behavior at runtime in response to changes within the system or in its execution environment. The fulfillment of the system requirements needs to be guaranteed even in the presence of adverse conditions and adaptations. Thus, a key challenge for self-adaptive software systems is assurance. Traditionally, confidence in the correctness of a system is gained through a variety of activities and processes performed at development time, such as design analysis and testing. In the presence of selfadaptation, however, some of the assurance tasks may need to be performed at runtime. This need calls for the development of techniques that enable continuous assurance throughout the software life cycle. Fundamental to the development of runtime assurance techniques is research into the use of models at runtime (M@RT). This chapter explores the state of the art for usingM@RT to address the assurance of self-adaptive software systems. It defines what information can be captured by M@RT, specifically for the purpose of assurance, and puts this definition into the context of existing work. We then outline key research challenges for assurance at runtime and characterize assurance methods. The chapter concludes with an exploration of selected application areas where M@RT could provide significant benefits beyond existing assurance techniques for adaptive systems.

cs.SE↗