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Lorenz, Jeanette Miriam

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Variational Quantum Circuit Design for Quantum Reinforcement Learning on Continuous Environments

2024 , Kruse, Georg , Dragan, Theodora-Augustina , Wille, Robert , Lorenz, Jeanette Miriam

Quantum Reinforcement Learning (QRL) emerged as a branch of reinforcement learning (RL) that uses quantum submodules in the architecture of the algorithm. One branch of QRL focuses on the replacement of neural networks (NN) by variational quantum circuits (VQC) as function approximators. Initial works have shown promising results on classical environments with discrete action spaces, but many of the proposed architectural design choices of the VQC lack a detailed investigation. Hence, in this work we investigate the impact of VQC design choices such as angle embedding, encoding block architecture and postprocessesing on the training capabilities of QRL agents. We show that VQC design greatly influences training performance and heuristically derive enhancements for the analyzed components. Additionally, we show how to design a QRL agent in order to solve classical environments with continuous action spaces and benchmark our agents against classical feed-forward NNs.

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Quantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Architecture and Optimizer Choices

2023 , Dragan, Theodora-Augustina , Monnet, Maureen , Mendl, Christian B. , Lorenz, Jeanette Miriam

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Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem

2023 , Palackal, Lilly , Poggel, Benedikt , Wulff, Matthias , Ehm, Hans , Lorenz, Jeanette Miriam , 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.

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Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness

2023 , Franco, Nicola , Wollschläger, Tom , Günnemann, Stephan , Poggel, Benedikt , Lorenz, Jeanette Miriam

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.

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Diffusion Denoised Smoothing for Certified and Adversarial Robust Out-Of-Distribution

2023 , Franco, Nicola , Korth, Daniel , Lorenz, Jeanette Miriam , Roscher, Karsten , 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

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Quantum Robustness Verification: A Hybrid Quantum-Classical Neural Network Certification Algorithm

2022 , Franco, Nicola , Wollschläger, Tom , Gao, Nicholas , Lorenz, Jeanette Miriam , 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.

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Benchmarking the Variational Quantum Eigensolver using different quantum hardware

2023 , Bentellis, Amine , Matic-Flierl, Andrea , Mendl, Christian B. , Lorenz, Jeanette Miriam

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.

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Recommending Solution Paths for Solving Optimization Problems with Quantum Computing

2023 , Poggel, Benedikt , Quetschlich, Nils , Burgholzer, Lukas , Wille, Robert , Lorenz, Jeanette Miriam

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and researchers alike. We propose a framework designed to identify and recommend the best-suited solution paths in an automated way. This introduces a novel abstraction layer that is required to make quantum-computing-assisted solution techniques accessible to end users without requiring a deeper knowledge of quantum technologies. State-of-the-art hybrid algorithms, encoding and decomposition techniques can be integrated in a modular manner and evaluated using problem-specific performance metrics. Equally, tools for the graphical analysis of variational quantum algorithms are developed. Classical, fault tolerant quantum and quantum-inspired methods can be included as well to ensure a fair comparison resulting in useful solution paths. We demonstrate and validate our approach on a selected set of options and illustrate its application on the capacitated vehicle routing problem (CVRP). We also identify crucial requirements and the major design challenges for the proposed abstraction layer within a quantum-assisted solution workflow for optimization problems.

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On Quantum Computing for Neural Network Robustness Verification

2022 , Franco, Nicola , Wollschläger, Tom , Gao, Nicholas , Lorenz, Jeanette Miriam , Günnemann, Stephan

In recent years, a multitude of approaches to certify the prediction of neural networks have been proposed. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified. For this reason, we propose to leverage the computational power of quantum computing for the robustness verification of neural networks. Further, we introduce a new Hybrid Quantum-Classical Robustness Algorithm for Neural network verification (HQ-CRAN). By applying Benders decomposition we split the verification problem into a quadratic unconstrained binary optimization and a linear program which we solve with quantum and classical computers, respectively. Further, we 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 provide bounds on the minimum number of qubits necessary to obtain a reasonable approximation. Finally, we evaluate our method on quantum hardware.

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