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Lorenz, Jeanette Miriam

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  • Publication
    Benchmarking Quantum Generative Learning: A Study on Scalability and Noise Resilience using QUARK
    ( 2024)
    Kiwit, Florian J.
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    Wolf, Maximilian A.
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    Marso, Marwa
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    Ross, Philipp
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    Lorenz, Jeanette Miriam orcid-logo
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    Riofrío, Carlos A.
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    Luckow, Andre
    Quantum computing promises a disruptive impact on machine learning algorithms, taking advantage of the exponentially large Hilbert space available. However, it is not clear how to scale quantum machine learning (QML) to industrial-level applications. This paper investigates the scalability and noise resilience of quantum generative learning applications. We consider the training performance in the presence of statistical noise due to finite-shot noise statistics and quantum noise due to decoherence to analyze the scalability of QML methods. We employ rigorous benchmarking techniques to track progress and identify challenges in scaling QML algorithms, and show how characterization of QML systems can be accelerated, simplified, and made reproducible when the QUARK framework is used. We show that QGANs are not as affected by the curse of dimensionality as QCBMs and to which extent QCBMs are resilient to noise.
  • Publication
    Variational Quantum Circuit Design for Quantum Reinforcement Learning on Continuous Environments
    ( 2024)
    Kruse, Georg
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    Dragan, Theodora-Augustina
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    Wille, Robert
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    Lorenz, Jeanette Miriam orcid-logo
    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.
  • Publication
    A Comparative Study on Solving Optimization Problems with Exponentially Fewer Qubits
    ( 2024)
    Winderl, David
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    Franco, Nicola
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    Lorenz, Jeanette Miriam orcid-logo
    Variational 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.
  • 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
    The Effect of Data Encoding on Quantum Convolutional Neural Networks
    ( 2023)
    Chaabani, Nermine
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    Dragan, Theodora-Augustina
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    Lorenz, Jeanette Miriam orcid-logo
    Quantum 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.
  • 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
    Optimizing hyperparameters using the geometric difference
    ( 2023)
    Egginger, Sebastian
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    Sakhnenko, Alona
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    Runge, Xiomara
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    Lorenz, Jeanette Miriam orcid-logo
    Quantum kernel methods (QKM) are a promising method in Quantum machine learning (QML) thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their potential for a quantum advantage. To do so, earlier works developed the geometric difference, which can be understood as a closeness measure between two kernel-based ML approaches, most importantly between a quantum kernel and classical kernel. This metric links the quantum and classical model complexities. Therefore, it raises the question of whether the geometric difference, based on its relation to model complexity, can be a useful tool in evaluations other than the potential for quantum advantage.
  • Publication
    Quantum-enhanced AI in medicine
    ( 2023)
    Lorenz, Jeanette Miriam orcid-logo
    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.