Marco Roth

Paul-Amaury Matt, Rosina Ziegler, Danilo Brajovic et al.

Our goal in this paper is to automatically extract a set of decision rules (rule set) that best explains a classification data set. First, a large set of decision rules is extracted from a set of decision trees trained on the data set. The rule set should be concise, accurate, have a maximum coverage and minimum number of inconsistencies. This problem can be formalized as a modified version of the weighted budgeted maximum coverage problem, known to be NP-hard. To solve the combinatorial optimization problem efficiently, we introduce a nested genetic algorithm which we then use to derive explanations for ten public data sets.

Frederic Rapp, Marco Roth

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient feature map and careful regularization of the Gram matrix, we demonstrate that the variance information of the resulting quantum Gaussian process can be preserved. We also show that quantum Gaussian processes can be used as a surrogate model for Bayesian optimization, a task that critically relies on the variance of the surrogate model. To demonstrate the performance of this quantum Bayesian optimization algorithm, we apply it to the hyperparameter optimization of a machine learning model which performs regression on a real-world dataset. We benchmark the quantum Bayesian optimization against its classical counterpart and show that quantum version can match its performance.

David A. Kreplin, Marco Roth

Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations, thus introducing fundamental finite-sampling noise even on error-free quantum computers. We reduce this noise by introducing the variance regularization, a technique for reducing the variance of the expectation value during the quantum model training. This technique requires no additional circuit evaluations if the QNN is properly constructed. Our empirical findings demonstrate the reduced variance speeds up the training and lowers the output noise as well as decreases the number of necessary evaluations of gradient circuits. This regularization method is benchmarked on the regression of multiple functions and the potential energy surface of water. We show that in our examples, it lowers the variance by an order of magnitude on average and leads to a significantly reduced noise level of the QNN. We finally demonstrate QNN training on a real quantum device and evaluate the impact of error mitigation. Here, the optimization is feasible only due to the reduced number of necessary shots in the gradient evaluation resulting from the reduced variance.

Jan Schnabel, Marco Roth

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights. Benchmarking these methods is crucial to gain robust insights and to understand their practical utility. In this work, we present a comprehensive large-scale study examining QKMs based on fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) across a manifold of design choices. Our investigation encompasses both classification and regression tasks for five dataset families and 64 datasets, systematically comparing the use of FQKs and PQKs quantum support vector machines and kernel ridge regression. This resulted in over 20,000 models that were trained and optimized using a state-of-the-art hyperparameter search to ensure robust and comprehensive insights. We delve into the importance of hyperparameters on model performance scores and support our findings through rigorous correlation analyses. Additionally, we provide an in-depth analysis addressing the design freedom of PQKs and explore the underlying principles responsible for learning. Our goal is not to identify the best-performing model for a specific task but to uncover the mechanisms that lead to effective QKMs and reveal universal patterns.

David A. Kreplin, Moritz Willmann, Jan Schnabel et al.

sQUlearn introduces a user-friendly, NISQ-ready Python library for quantum machine learning (QML), designed for seamless integration with classical machine learning tools like scikit-learn. The library's dual-layer architecture serves both QML researchers and practitioners, enabling efficient prototyping, experimentation, and pipelining. sQUlearn provides a comprehensive toolset that includes both quantum kernel methods and quantum neural networks, along with features like customizable data encoding strategies, automated execution handling, and specialized kernel regularization techniques. By focusing on NISQ-compatibility and end-to-end automation, sQUlearn aims to bridge the gap between current quantum computing capabilities and practical machine learning applications. The library provides substantial flexibility, enabling quick transitions between the underlying quantum frameworks Qiskit and PennyLane, as well as between simulation and running on actual hardware.

Roberto Flórez-Ablan, Marco Roth, Jan Schnabel

Quantum kernels (QK) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential concentration phenomenon, which can impair generalization. A common strategy to alleviate this is bandwidth tuning, which involves rescaling data points in the quantum model to improve generalization. In this work, we numerically demonstrate that optimal bandwidth tuning results in QKs that closely resemble radial basis function (RBF) kernels, leading to a lack of quantum advantage over classical methods. Moreover, we reveal that the size of optimal bandwidth tuning parameters further simplifies QKs, causing them to behave like polynomial kernels, corresponding to a low-order Taylor approximation of a RBF kernel. We thoroughly investigate this for fidelity quantum kernels and projected quantum kernels using various data encoding circuits across several classification datasets. We provide numerical evidence and derive a simple analytical model that elucidates how bandwidth tuning influences key quantities in classification tasks. Overall, our findings shed light on the mechanisms that render QK methods classically tractable.

Manuel Hagelüken, Marco F. Huber, Marco Roth

Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network and a conventional neural network and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: $H_2$ with four orbitals, LiH with five orbitals, and $H_4$ with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and neural networks) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.

Marco Roth, David A. Kreplin, Daniel Basilewitsch et al.

Automated Machine Learning (AutoML) has significantly advanced the efficiency of ML-focused software development by automating hyperparameter optimization and pipeline construction, reducing the need for manual intervention. Quantum Machine Learning (QML) offers the potential to surpass classical machine learning (ML) capabilities by utilizing quantum computing. However, the complexity of QML presents substantial entry barriers. We introduce \emph{AutoQML}, a novel framework that adapts the AutoML approach to QML, providing a modular and unified programming interface to facilitate the development of QML pipelines. AutoQML leverages the QML library sQUlearn to support a variety of QML algorithms. The framework is capable of constructing end-to-end pipelines for supervised learning tasks, ensuring accessibility and efficacy. We evaluate AutoQML across four industrial use cases, demonstrating its ability to generate high-performing QML pipelines that are competitive with both classical ML models and manually crafted quantum solutions.

Frederic Rapp, David A. Kreplin, Marco F. Huber et al.

Quantum machine learning models use encoding circuits to map data into a quantum Hilbert space. While it is well known that the architecture of these circuits significantly influences core properties of the resulting model, they are often chosen heuristically. In this work, we present a novel approach using reinforcement learning techniques to generate problem-specific encoding circuits to improve the performance of quantum machine learning models. By specifically using a model-based reinforcement learning algorithm, we reduce the number of necessary circuit evaluations during the search, providing a sample-efficient framework. In contrast to previous search algorithms, our method uses a layered circuit structure that significantly reduces the search space. Additionally, our approach can account for multiple objectives such as solution quality, hardware restrictions and circuit depth. We benchmark our tailored circuits against various reference models, including models with problem-agnostic circuits and classical models. Our results highlight the effectiveness of problem-specific encoding circuits in enhancing QML model performance.