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Lorenz, Jeanette Miriam

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  • Publication
    Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness
    ( 2023)
    Franco, Nicola
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    Wollschläger, Tom
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    Günnemann, Stephan
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    Poggel, Benedikt orcid-logo
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    Lorenz, Jeanette Miriam orcid-logo
    Emerging quantum computing technologies, such as Noisy Intermediate-Scale Quantum (NISQ) devices, offer potential advancements in solving mathematical optimization problems. However, limitations in qubit availability, noise, and errors pose challenges for practical implementation. In this study, we examine two decomposition methods for Mixed-Integer Linear Programming (MILP) designed to reduce the original problem size and utilize available NISQ devices more efficiently. We concentrate on breaking down the original problem into smaller subproblems, which are then solved iteratively using a combined quantum-classical hardware approach. We conduct a detailed analysis for the decomposition of MILP with Benders and Dantzig-Wolfe methods. In our analysis, we show that the number of qubits required to solve Benders is exponentially large in the worst-case, while remains constant for Dantzig-Wolfe. Additionally, we leverage Dantzig-Wolfe decomposition on the use-case of certifying the robustness of ReLU networks. Our experimental results demonstrate that this approach can save up to 90% of qubits compared to existing methods on quantum annealing and gate-based quantum computers.
  • Publication
    Benchmarking the Variational Quantum Eigensolver using different quantum hardware
    ( 2023)
    Bentellis, Amine
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    Matic-Flierl, Andrea
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    Mendl, Christian B.
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    Lorenz, Jeanette Miriam orcid-logo
    The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy Intermediate-Scale Quantum (NISQ) era. The ability for a quantum computer to simulate electronic structures with high accuracy would have a profound impact on material and biochemical science with potential applications e.g., to the development of new drugs. However, considering the variety of quantum hardware architectures, it is still uncertain which hardware concept is most suited to execute the VQE for e.g., the simulation of molecules. Aspects to consider here are the required connectivity of the quantum circuit used, the size and the depth and thus the susceptibility to noise effects. Besides theo-retical considerations, empirical studies using available quantum hardware may help to clarify the question of which hardware technology might be better suited for a certain given application and algorithm. Going one step into this direction, within this work, we present results using the VQE for the simulation of the hydrogen molecule, comparing superconducting and ion trap quantum computers. The experiments are carried out with a standardized setup of ansatz and optimizer, selected to reduce the number of required iterations. The findings are analyzed considering different quantum processor types, calibration data as well as the depth and gate counts of the circuits required for the different hardware concepts after transpilation.
  • Publication
    Quantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Quantum Architecture Choices
    ( 2023)
    Dragan, Theodora-Augustina
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    Monnet, Maureen
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    Mendl, Christian B.
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    Lorenz, Jeanette Miriam orcid-logo
    Quantum reinforcement learning (QRL) models augment classical reinforcement learning schemes with quantum-enhanced kernels. Different proposals on how to construct such models empirically show a promising performance. In particular, these models might offer a reduced parameter count and shorter times to reach a solution than classical models. It is however presently unclear how these quantum-enhanced kernels as subroutines within a reinforcement learning pipeline need to be constructed to indeed result in an improved performance in comparison to classical models. In this work we exactly address this question. First, we propose a hybrid quantum-classical reinforcement learning model that solves a slippery stochastic frozen lake, an environment considerably more difficult than the deterministic frozen lake. Secondly, different quantum architectures are studied as options for this hybrid quantum-classical reinforcement learning model, all of them well-motivated by the literature. They a ll show very promising performances with respect to similar classical variants. We further characterize these choices by metrics that are relevant to benchmark the power of quantum circuits, such as the entanglement capability, the expressibility, and the information density of the circuits. However, we find that these typical metrics do not directly predict the performance of a QRL model.
  • Publication
    Diffusion Denoised Smoothing for Certified and Adversarial Robust Out-Of-Distribution
    ( 2023)
    Franco, Nicola
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    Korth, Daniel
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    Lorenz, Jeanette Miriam orcid-logo
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    Roscher, Karsten
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    Günnemann, Stephan
    As the use of machine learning continues to expand, the importance of ensuring its safety cannot be overstated. A key concern in this regard is the ability to identify whether a given sample is from the training distribution, or is an "Out-Of-Distribution" (OOD) sample. In addition, adversaries can manipulate OOD samples in ways that lead a classifier to make a confident prediction. In this study, we present a novel approach for certifying the robustness of OOD detection within a ℓ2-norm around the input, regardless of network architecture and without the need for specific components or additional training. Further, we improve current techniques for detecting adversarial attacks on OOD samples, while providing high levels of certified and adversarial robustness on in-distribution samples. The average of all OOD detection metrics on CIFAR10/100 shows an increase of ∼ 13%/5% relative to previous approaches. Code: https://github.com/FraunhoferIKS/distro
  • Publication
    Pooling Techniques in Hybrid Quantum-Classical Convolutional Neural Networks
    ( 2023)
    Monnet, Maureen
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    Gebran, Hanady
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    Matic-Flierl, Andrea
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    Kiwit, Florian
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    Schachtner, Balthasar
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    Bentellis, Amine
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    Lorenz, Jeanette Miriam orcid-logo
    Quantum machine learning has received significant interest in recent years, with theoretical studies showing that quantum variants of classical machine learning algorithms can provide good generalization from small training data sizes. However, there are notably no strong theoretical insights about what makes a quantum circuit design better than another, and comparative studies between quantum equivalents have not been done for every type of classical layers or techniques crucial for classical machine learning. Particularly, the pooling layer within convolutional neural networks is a fundamental operation left to explore. Pooling mechanisms significantly improve the performance of classical machine learning algorithms by playing a key role in reducing input dimensionality and extracting clean features from the input data. In this work, an in-depth study of pooling techniques in hybrid quantum-classical convolutional neural networks (QCCNNs) for classifying 2D medical images is performed. The performance of four different quantum and hybrid pooling techniques is studied: mid-circuit measurements, ancilla qubits with controlled gates, modular quantum pooling blocks and qubit selection with classical postprocessing. We find similar or better performance in comparison to an equivalent classical model and QCCNN without pooling and conclude that it is promising to study architectural choices in QCCNNs in more depth for future applications.
  • Publication
    Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem
    ( 2023)
    Palackal, Lilly
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    Poggel, Benedikt orcid-logo
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    Wulff, Matthias
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    Ehm, Hans
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    Lorenz, Jeanette Miriam orcid-logo
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    Mendl, Christian B.
    Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution, although the question remains open as to whether Noisy Intermediate-Scale Quantum (NISQ) devices can achieve a practical advantage compared to classical heuristics. The most prominent algorithms proposed to solve combinatorial optimization problems in the NISQ era are the Quantum Approximate Optimization Algorithm (QAOA) and the more general Variational Quantum Eigensolver (VQE). However, implementing them in a way that reliably provides high-quality solutions is challenging, even for toy examples. In this work, we discuss decomposition and formulation aspects of the CVRP and propose an application-driven way to measure solution quality. Considering current hardware constraints, we reduce the CVRP to a clustering phase and a set of TSPs. For the TSP, we extensively test both QAOA and VQE and investigate the influence of various hyperparameters, such as the classical optimizer choice and strength of constraint penalization. Results of QAOA are generally of limited quality because the algorithm does not reach the energy threshold for feasible TSP solutions, even when considering various extensions such as recursive and constraint-preserving mixer QAOA. On the other hand, the VQE reaches the energy threshold and shows a better performance. Our work outlines the obstacles to quantum-assisted solutions for real-world optimization problems and proposes perspectives on how to overcome them.
  • Publication
    Quantum Robustness Verification: A Hybrid Quantum-Classical Neural Network Certification Algorithm
    ( 2022)
    Franco, Nicola
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    Wollschläger, Tom
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    Gao, Nicholas
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    Lorenz, Jeanette Miriam orcid-logo
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    Günnemann, Stephan
    In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.
  • Publication
    Quantencomputing für industrielle Softwareanwendungen
    ( 2021)
    Lorenz, Jeanette Miriam orcid-logo
    Obwohl Quantencomputer aktuell noch nicht leistungsstark genug sind um in der Industrie breite Anwendung zu finden, wird vorhergesagt, dass Quantencomputing in vielen Feldern innerhalb der nächsten 10 Jahre zu tiefgehenden Veränderungen führen wird. Dabei haben Quantencomputer aufgrund ihrer quantenmechanischen Eigenschaften das Potential sowohl klassische Software-Algorithmen deutlich zu beschleunigen, wie auch komplett neue Problemklassen zu erschließen. Beispiele für Anwendungen sind eine effizientere Simulation von Molekülen für Katalysatoren, Enzyme oder Medikamenten, Simulation von Batterien im Energiesektor oder für das autonome Fahren, oder auch die Lösung komplexer Optimierungsprobleme beispielsweise im Logistiksektor. Auch im Bereich der künstlichen Intelligenz kann das Quantencomputing zu tiefgreifenden Veränderungen führen, beispielsweise durch ein deutlich effizienteres Training von neuronalen Netzen. Bei diesen vielfältigen Anwendungsmöglichkeiten und den zugleich zu erwartenden disruptiven Veränderungen ist es notwendig frühzeitig zu gewährleisten, dass Quantencomputing verlässlich und für die Endanwender sicher eingesetzt werden kann. In diesem Vortrag wird zunächst erläutert, warum angenommen wird, dass Quantencomputing einige Softwarealgorithmen deutlich effizienter gestalten kann, und sodann einige der Anwendungsfelder und Anwendungsbeispiele diskutiert. Abschließend wird ein Ausblick über die zu erwartende Entwicklung des Quantencomputings in den nächsten Jahren gegeben.