arXiv subjects

Thore Gerlach

Publications and source records attributed to Thore Gerlach.

At least 19 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↗

arXiv2026

Beyond Reinforcement Learning: Fast and Scalable Quantum Circuit Synthesis

Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the underlying combinatorial search space. Existing approaches suffer from misaligned optimization objectives, substantial training costs and limited generalization across different qubit counts. We mitigate these limitations by using supervised learning to approximate the minimum description length of residual unitaries and combining this estimate with stochastic beam search to identify near optimal gate sequences. Our method relies on a lightweight model with zero-shot generalization, substantially reducing training overhead compared to prior baselines. Across multiple benchmarks, we achieve faster wall-clock synthesis times while exceeding state-of-the-art methods in terms of success rate for complex circuits.

quant-ph↗

arXiv2026

WARP Logic Neural Networks

Fast and efficient AI inference is increasingly important, and recent models that directly learn low-level logic operations have achieved state-of-the-art performance. However, existing logic neural networks incur high training costs, introduce redundancy or rely on approximate gradients, which limits scalability. To overcome these limitations, we introduce WAlsh Relaxation for Probabilistic (WARP) logic neural networks -- a novel gradient-based framework that efficiently learns combinations of hardware-native logic blocks. We show that WARP yields the most parameter-efficient representation for exactly learning Boolean functions and that several prior approaches arise as restricted special cases. Training is improved by introducing learnable thresholding and residual initialization, while we bridge the gap between relaxed training and discrete logic inference through stochastic smoothing. Experiments demonstrate faster convergence than state-of-the-art baselines, while scaling effectively to deeper architectures and logic functions with higher input arity.

cs.LG↗

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.

quant-ph↗

arXiv2025

Quantum Boltzmann Machines for Sample-Efficient Reinforcement Learning

We introduce theoretically grounded Continuous Semi-Quantum Boltzmann Machines (CSQBMs) that supports continuous-action reinforcement learning. By combining exponential-family priors over visible units with quantum Boltzmann distributions over hidden units, CSQBMs yield a hybrid quantum-classical model that reduces qubit requirements while retaining strong expressiveness. Crucially, gradients with respect to continuous variables can be computed analytically, enabling direct integration into Actor-Critic algorithms. Building on this, we propose a continuous Q-learning framework that replaces global maximization by efficient sampling from the CSQBM distribution, thereby overcoming instability issues in continuous control.

cs.LG↗

arXiv2025

WARP-LUTs -- Walsh-Assisted Relaxation for Probabilistic Look Up Tables

Fast and efficient machine learning is of growing interest to the scientific community and has spurred significant research into novel model architectures and hardware-aware design. Recent hard? and software co-design approaches have demonstrated impressive results with entirely multiplication-free models. Differentiable Logic Gate Networks (DLGNs), for instance, provide a gradient-based framework for learning optimal combinations of low-level logic gates, setting state-of-the-art trade-offs between accuracy, resource usage, and latency. However, these models suffer from high computational cost during training and do not generalize well to logic blocks with more inputs. In this work, we introduce Walsh-Assisted Relaxation for Probabilistic Look-Up Tables (WARP-LUTs) - a novel gradient-based method that efficiently learns combinations of logic gates with substantially fewer trainable parameters. We demonstrate that WARP-LUTs achieve significantly faster convergence on CIFAR-10 compared to DLGNs, while maintaining comparable accuracy. Furthermore, our approach suggests potential for extension to higher-input logic blocks, motivating future research on extremely efficient deployment on modern FPGAs and its real-time science applications.

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".

quant-ph↗

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

Standardization of Multi-Objective QUBOs

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

cs.LG↗

arXiv2025

Hybrid Quantum-Classical Multi-Agent Pathfinding

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-andcut-and-price. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulationsand state-of-the-art MAPF solvers.

cs.AI↗

arXiv2024

Dynamic Range Reduction via Branch-and-Bound

The demand for high-performance computing in machine learning and artificial intelligence has led to the development of specialized hardware accelerators like Tensor Processing Units (TPUs), Graphics Processing Units (GPUs), and Field-Programmable Gate Arrays (FPGAs). A key strategy to enhance these accelerators is the reduction of precision in arithmetic operations, which increases processing speed and lowers latency - crucial for real-time AI applications. Precision reduction minimizes memory bandwidth requirements and energy consumption, essential for large-scale and mobile deployments, and increases throughput by enabling more parallel operations per cycle, maximizing hardware resource utilization. This strategy is equally vital for solving NP-hard quadratic unconstrained binary optimization (QUBO) problems common in machine learning, which often require high precision for accurate representation. Special hardware solvers, such as quantum annealers, benefit significantly from precision reduction. This paper introduces a fully principled Branch-and-Bound algorithm for reducing precision needs in QUBO problems by utilizing dynamic range as a measure of complexity. Experiments validate our algorithm's effectiveness on an actual quantum annealer.

cs.LG↗

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↗

arXiv2023

FPGA-Placement via Quantum Annealing

Field-Programmable Gate Arrays (FPGAs) have asserted themselves as vital assets in contemporary computing by offering adaptable, reconfigurable hardware platforms. FPGA-based accelerators incubate opportunities for breakthroughs in areas, such as real-time data processing, machine learning or cryptography -- to mention just a few. The procedure of placement -- determining the optimal spatial arrangement of functional blocks on an FPGA to minimize communication delays and enhance performance -- is an NP-hard problem, notably requiring sophisticated algorithms for proficient solutions. Clearly, improving the placement leads to a decreased resource utilization during the implementation phase. Adiabatic quantum computing (AQC), with its capability to traverse expansive solution spaces, has potential for addressing such combinatorial problems. In this paper, we re-formulate the placement problem as a series of so called quadratic unconstrained binary optimization (QUBO) problems which are subsequently solved via AQC. Our novel formulation facilitates a straight-forward integration of design constraints. Moreover, the size of the sub-problems can be conveniently adapted to the available hardware capabilities. Beside the sole proposal of a novel method, we ask whether contemporary quantum hardware is resilient enough to find placements for real-world-sized FPGAs. A numerical evaluation on a D-Wave Advantage 5.4 quantum annealer suggests that the answer is in the affirmative.

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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

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.

quant-ph↗

arXiv2023

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.

quant-ph↗

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↗