PD Dr.

Lorenz, Jeanette Miriam

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  • Publication
    The Effect of Data Encoding on Quantum Convolutional Neural Networks
    ( 2023)
    Chaabani, Nermine
    ;
    Dragan, Theodora-Augustina
    ;
    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
    Quantum Reinforcement Learning for Solving a Stochastic Frozen Lake Environment and the Impact of Quantum Architecture Choices
    ( 2023)
    Dragan, Theodora-Augustina
    ;
    Monnet, Maureen
    ;
    Mendl, Christian B.
    ;
    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.