arXiv subjects

Sascha Mücke

Publications and source records attributed to Sascha Mücke.

18 recordsLinked to original sources

arXiv2026

Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform

We present a novel slack-free, penalty-based framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO) on near-term quantum annealing hardware. Given a user-chosen penalty function that most naturally captures a constraint---typically non-quadratic, such as a Heaviside-function surrogate---and a target probability measure over the Boolean hypercube, our method returns the weighted least-squares projection of the chosen penalty function onto the subspace spanned by linear and quadratic Walsh--Fourier characters that correspond to physically realizable couplings on the target hardware graph. Within this restricted family, the resulting quadratic surrogate is uniquely and optimally determined by the normal equations: unlike state-of-the-art approaches, it introduces no per-constraint penalty coefficients to tune and avoids dense all-pairs couplings by construction. Two practical consequences follow. First, the projected penalty respects device connectivity, reducing chain lengths and physical-qubit overhead after minor embedding. Second, we show empirically that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space. This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.

quant-ph↗

arXiv2025

Quadratic Continuous Quantum Optimization

Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.

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arXiv2025

On the Impact of Weight Discretization in QUBO-Based SVM Training

Training Support Vector Machines (SVMs) can be formulated as a QUBO problem, enabling the use of quantum annealing for model optimization. In this work, we study how the number of qubits - linked to the discretization level of dual weights - affects predictive performance across datasets. We compare QUBO-based SVM training to the classical LIBSVM solver and find that even low-precision QUBO encodings (e.g., 1 bit per parameter) yield competitive, and sometimes superior, accuracy. While increased bit-depth enables larger regularization parameters, it does not always improve classification. Our findings suggest that selecting the right support vectors may matter more than their precise weighting. Although current hardware limits the size of solvable QUBOs, our results highlight the potential of quantum annealing for efficient SVM training as quantum devices scale.

cs.LG↗

arXiv2025

Kernel $k$-Medoids as General Vector Quantization

Vector Quantization (VQ) is a widely used technique in machine learning and data compression, valued for its simplicity and interpretability. Among hard VQ methods, $k$-medoids clustering and Kernel Density Estimation (KDE) approaches represent two prominent yet seemingly unrelated paradigms -- one distance-based, the other rooted in probability density matching. In this paper, we investigate their connection through the lens of Quadratic Unconstrained Binary Optimization (QUBO). We compare a heuristic QUBO formulation for $k$-medoids, which balances centrality and diversity, with a principled QUBO derived from minimizing Maximum Mean Discrepancy in KDE-based VQ. Surprisingly, we show that the KDE-QUBO is a special case of the $k$-medoids-QUBO under mild assumptions on the kernel's feature map. This reveals a deeper structural relationship between these two approaches and provides new insight into the geometric interpretation of the weighting parameters used in QUBO formulations for VQ.

cs.LG↗

arXiv2025

QUBOLite: A lightweigth Python toolkit for QUBO

We present QUBOLite, a Python package for the creation, manipulation, analysis, and solution of Quadratic Unconstrained Binary Optimization (QUBO) instances. Built as a thin wrapper around NumPy arrays, QUBOLite combines efficient numerical operations with high-level abstractions for tasks ranging from instance generation to preprocessing, analysis, and solving strategies, both exact and approximate. The package includes implementations of the QPRO+ algorithm by Glover et al. for identifying strong persistencies, dynamic range reduction heuristics, and an expressive system for partial assignments (clamping) enabling implicit variable assignment. The package is available on GitHub and the official Python package repository.

cs.MS↗

arXiv2025

Quantum Adiabatic Generation of Human-Like Passwords

Generative Artificial Intelligence (GenAI) for Natural Language Processing (NLP) is the predominant AI technology to date. An important perspective for Quantum Computing (QC) is the question whether QC has the potential to reduce the vast resource requirements for training and operating GenAI models. While large-scale generative NLP tasks are currently out of reach for practical quantum computers, the generation of short semantic structures such as passwords is not. Generating passwords that mimic real user behavior has many applications, for example to test an authentication system against realistic threat models. Classical password generation via deep learning have recently been investigated with significant progress in their ability to generate novel, realistic password candidates. In the present work we investigate the utility of adiabatic quantum computers for this task. More precisely, we study different encodings of token strings and propose novel approaches based on the Quadratic Unconstrained Binary Optimization (QUBO) and the Unit-Disk Maximum Independent Set (UD-MIS) problems. Our approach allows us to estimate the token distribution from data and adiabatically prepare a quantum state from which we eventually sample the generated passwords via measurements. Our results show that relatively small samples of 128 passwords, generated on the QuEra Aquila 256-qubit neutral atom quantum computer, contain human-like passwords such as "Tunas200992" or "teedem28iglove".

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arXiv2025

Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning

Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of the explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we apply the well-established concept of Shapley values. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.

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arXiv2024

Predicting Machining Stability with a Quantum Regression Model

In this article, we propose a novel quantum regression model by extending the Real-Part Quantum SVM. We apply our model to the problem of stability limit prediction in milling processes, a key component in high-precision manufacturing. To train our model, we use a custom data set acquired by an extensive series of milling experiments using different spindle speeds, enhanced with a custom feature map. We show that the resulting model predicts the stability limits observed in our physical setup accurately, demonstrating that quantum computing is capable of deploying ML models for real-world applications.

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arXiv2024

Investigating the Relation Between Problem Hardness and QUBO Properties

Combinatorial optimization problems, integral to various scientific and industrial applications, often vary significantly in their complexity and computational difficulty. Transforming such problems into Quadratic Unconstrained Binary Optimization (QUBO) has regained considerable research attention in recent decades due to the central role of QUBO in Quantum Annealing. This work aims to shed some light on the relationship between the problems' properties. In particular, we examine how the spectral gap of the QUBO formulation correlates with the original problem, since it has an impact on how efficiently it can be solved on quantum computers. We analyze two well-known problems from Machine Learning, namely Clustering and Support Vector Machine (SVM) training, regarding the spectral gaps of their respective QUBO counterparts. An empirical evaluation provides interesting insights, showing that the spectral gap of Clustering QUBO instances positively correlates with data separability, while for SVM QUBO the opposite is true.

quant-ph↗

arXiv2024

A Simple QUBO Formulation of Sudoku

This article describes how to solve Sudoku puzzles using Quadratic Unconstrained Binary Optimization (QUBO). To this end, a QUBO instance with 729 variables is constructed, encoding a Sudoku grid with all constraints in place, which is then partially assigned to account for clues. The resulting instance can be solved with a Quantum Annealer, or any other strategy, to obtain the fully filled-out Sudoku grid. Moreover, as all valid solutions have the same energy, the QUBO instance can be used to sample uniformly from the space of valid Sudoku grids. We demonstrate the described method using both a heuristic solver and a Quantum Annealer.

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arXiv2023

On the effects of biased quantum random numbers on the initialization of artificial neural networks

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

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arXiv2023

Efficient Light Source Placement using Quantum Computing

NP-hard problems regularly come up in video games, with interesting connections to real-world problems. In the game Minecraft, players place torches on the ground to light up dark areas. Placing them in a way that minimizes the total number of torches to save resources is far from trivial. In this paper, we use Quantum Computing to approach this problem. To this end, we derive a QUBO formulation of the torch placement problem, which we uncover to be very similar to another NP-hard problem. We employ a solution strategy that involves learning Lagrangian weights in an iterative process, adding to the ever growing toolbox of QUBO formulations. Finally, we perform experiments on real quantum hardware using real game data to demonstrate that our approach yields good torch placements.

quant-ph↗

arXiv2023

Faster QUBO Brute-Force Solving using Gray Code

This article describes an improved brute-force solving strategy for Quadratic Unconstrained Binary Optimization (QUBO) problems that is faster than naive approaches and easily parallelizable. It exploits the Gray code ordering of natural numbers to allow for a more efficient evaluation of the QUBO objective function. The implementation in Python is discussed in detail, and an additional C implementation is provided.

cs.DS↗

arXiv2023

Optimum-Preserving QUBO Parameter Compression

Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware noise, the effective set of feasible parameter values is severely restricted. As a result, otherwise solvable problems become harder or even intractable. In this work, we study the implications of solving QUBO problems under limited precision. Specifically, it is shown that the problem's dynamic range has a crucial impact on the problem's robustness against distortions. We show this by formalizing the notion of preserving optima between QUBO instances and explore to which extend parameters can be modified without changing the set of minimizing solutions. Based on these insights, we introduce techniques to reduce the dynamic range of a given QUBO instance based on theoretical bounds of the minimal energy value. An experimental evaluation on random QUBO instances as well as QUBO-encoded Binary Clustering and Subset Sum problems show that our theoretical findings manifest in practice. Results on quantum annealing hardware show that the performance can be improved drastically when following our methodology.

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arXiv2023

Feature Selection on Quantum Computers

In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higherquality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark datasets. We observe competitive performance.

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arXiv2023

Shapley Values with Uncertain Value Functions

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.

cs.LG↗

arXiv2022

Yes We Care! -- Certification for Machine Learning Methods through the Care Label Framework

Machine learning applications have become ubiquitous. Their applications range from embedded control in production machines over process optimization in diverse areas (e.g., traffic, finance, sciences) to direct user interactions like advertising and recommendations. This has led to an increased effort of making machine learning trustworthy. Explainable and fair AI have already matured. They address the knowledgeable user and the application engineer. However, there are users that want to deploy a learned model in a similar way as their washing machine. These stakeholders do not want to spend time in understanding the model, but want to rely on guaranteed properties. What are the relevant properties? How can they be expressed to the stakeholder without presupposing machine learning knowledge? How can they be guaranteed for a certain implementation of a machine learning model? These questions move far beyond the current state of the art and we want to address them here. We propose a unified framework that certifies learning methods via care labels. They are easy to understand and draw inspiration from well-known certificates like textile labels or property cards of electronic devices. Our framework considers both, the machine learning theory and a given implementation. We test the implementation's compliance with theoretical properties and bounds.

cs.LG↗

arXiv2022

Quantum Circuit Evolution on NISQ Devices

Variational quantum circuits build the foundation for various classes of quantum algorithms. In a nutshell, the weights of a parametrized quantum circuit are varied until the empirical sampling distribution of the circuit is sufficiently close to a desired outcome. Numerical first-order methods are applied frequently to fit the parameters of the circuit, but most of the time, the circuit itself, that is, the actual composition of gates, is fixed. Methods for optimizing the circuit design jointly with the weights have been proposed, but empirical results are rather scarce. Here, we consider a simple evolutionary strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We evaluate our method both via simulation and on actual quantum hardware. Our benchmark problems include the transverse field Ising Hamiltonian and the Sherrington-Kirkpatrick spin model. Despite the shortcomings of current noisy intermediate-scale quantum hardware, we find only a minor slowdown on actual quantum machines compared to simulations. Moreover, we investigate which mutation operations most significantly contribute to the optimization. The results provide intuition on how randomized search heuristics behave on actual quantum hardware and lay out a path for further refinement of evolutionary quantum gate circuits.

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