Jonas Jäger

Jonas Jäger, Roman V. Krems

Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer.

Jonas Jäger, Gereon Reus, Joachim Denzler et al.

State-of-the-art computer vision approaches rely on huge amounts of annotated data. The collection of such data is a time consuming process since it is mainly performed by humans. The literature shows that semi-automatic annotation approaches can significantly speed up the annotation process by the automatic generation of annotation proposals to support the annotator. In this paper we present a framework that allows for a quick and flexible design of semi-automatic annotation pipelines. We show that a good design of the process will speed up the collection of annotations. Our contribution is a new approach to image annotation that allows for the combination of different annotation tools and machine learning algorithms in one process. We further present potential applications of our approach. The source code of our framework called LOST (Label Objects and Save Time) is available at: https://github.com/l3p-cv/lost.

Jonas Jäger, Paolo Braccia, Pablo Bermejo et al.

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.

Jonas Jäger, Philipp Elsässer, Elham Torabian

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.