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PublicationVariational Quantum Circuit Design for Quantum Reinforcement Learning on Continuous Environments( 2024)
;Wille, RobertQuantum 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 feedforward NNs. 
PublicationA Comparative Study on Solving Optimization Problems with Exponentially Fewer Qubits( 2024)
;Winderl, DavidVariational quantum optimization algorithms, such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an algorithm based on the VQE, which uses exponentially fewer qubits compared to the QAOA. We highlight the numerical instabilities generated by encoding the problem into the variational ansatz and propose a classical optimization procedure to find the ground state of the ansatz in fewer iterations with a better or similar objective. In addition, we propose a method to embed the linear interpolation of the MaxCut problem on a quantum device. Furthermore, we compare classical optimizers for this variational ansatz on quadratic unconstrained binary optimization and graph partitioning problems. 
PublicationBenchmarking the Variational Quantum Eigensolver using different quantum hardware( 2023)
;Bentellis, Amine ;MaticFlierl, Andrea ;Mendl, Christian B.The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy IntermediateScale 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 theoretical 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. 
PublicationEfficient MILP Decomposition in Quantum Computing for ReLU Network Robustness( 2023)
;Wollschläger, Tom ;Günnemann, StephanEmerging quantum computing technologies, such as Noisy IntermediateScale 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 MixedInteger 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 quantumclassical hardware approach. We conduct a detailed analysis for the decomposition of MILP with Benders and DantzigWolfe methods. In our analysis, we show that the number of qubits required to solve Benders is exponentially large in the worstcase, while remains constant for DantzigWolfe. Additionally, we leverage DantzigWolfe decomposition on the usecase 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 gatebased quantum computers. 
PublicationQuantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Quantum Architecture Choices( 2023)
;Monnet, Maureen ;Mendl, Christian B.Quantum reinforcement learning (QRL) models augment classical reinforcement learning schemes with quantumenhanced 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 quantumenhanced 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 quantumclassical 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 quantumclassical reinforcement learning model, all of them wellmotivated 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. 
PublicationQuantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Architecture and Optimizer Choices( 2023)
;Monnet, Maureen ;Mendl, Christian B. 
PublicationThe Effect of Data Encoding on Quantum Convolutional Neural Networks( 2023)
;Chaabani, NermineQuantum Convolutional Neural Networks (QCNNs) are hybrid solutions suggested by literature to achieve good generalization with less data. In this work, we investigate the effect of the data encoding choice on the QCNN architecture, where the classical convolutional layer is replaced by a variational quantum circuit (VQC). The task is binary classification of malign or benign ultrasound images of a medical dataset (BreastMNIST). We first investigate quantum metrics from literature such as normalized effective dimension, entanglement capability and expressibility, but find no clear correlation with performance. We also explore the idea of VQCs as Fourier series. The QCNN architecture may consist of multiple reuploading layers each consisting of data encoding and a trainable Ansatz. We perform numerical experiments by varying the data encoding to be the angle or higher order encoding up to four reuploading layers. We analyze the distribution of the Fourier coefficients in each case and find evidence that reinforces ideas from literature: the variance of the distribution increases with the number of layers and appears to reach a saturation at two layers in the univariate case, which indicates that the circuits do not have enough degrees of freedom to allow full control over the Fourier coefficients. This can be interpreted as noise induced in the circuit due to lack of degrees of freedom. A better understanding of encoding strategies is needed to design an alternative strategy that is resilient to this issue. The multivariate case, where different input combinations are considered is analyzed for up to six data reuploading layers. The same observation of increased variance persists, and a saturation is reached at four layers. We find that the best performing models exhibit a linear structure in the distribution of coefficients, corresponding to a fixed phase. This might be an indication that a fixed phase simplifies the problem’s optimization and requires further investigation. 
PublicationDiffusion Denoised Smoothing for Certified and Adversarial Robust OutOfDistribution( 2023)
;Korth, DanielGünnemann, StephanAs 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 "OutOfDistribution" (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 ℓ2norm 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 indistribution 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 
PublicationQuantum Neural Networks under Depolarization Noise: Exploring WhiteBox Attacks and Defenses( 2023)
;Winderl, DavidLeveraging the unique properties of quantum mechanics, Quantum Machine Learning (QML) promises computational breakthroughs and enriched perspectives where traditional systems reach their boundaries. However, similarly to classical machine learning, QML is not immune to adversarial attacks. Quantum adversarial machine learning has become instrumental in highlighting the weak points of QML models when faced with adversarial crafted feature vectors. Diving deep into this domain, our exploration shines light on the interplay between depolarization noise and adversarial robustness. While previous results enhanced robustness from adversarial threats through depolarization noise, our findings paint a different picture. Interestingly, adding depolarization noise discontinued the effect of providing further robustness for a multiclass classification scenario. Consolidating our findings, we conducted experiments with a multiclass classifier adversarially trained on gatebased quantum simulators, further elucidating this unexpected behavior. 
PublicationQuantumenhanced AI in medicine( 2023)Quantum computing is predicted as distruptive technologies with the capabilties to analyize complex patterns in data. The medical sector is a challenging field for applying artifical intelligence methods due to different reasons, but one of them being the limited amount of training data available. This talk describes how quantum computing might be able to address some of the open challenges in the sector of digital health, as in particular for the case where only limited training data is available.