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Lorenz, Jeanette Miriam

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Benchmarking Quantum Generative Learning: A Study on Scalability and Noise Resilience using QUARK

2024 , Kiwit, Florian J. , Wolf, Maximilian A. , Marso, Marwa , Ross, Philipp , Lorenz, Jeanette Miriam , Riofrío, Carlos A. , 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.

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The Effect of Data Encoding on Quantum Convolutional Neural Networks

2023 , Chaabani, Nermine , Dragan, Theodora-Augustina , Lorenz, Jeanette Miriam

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.

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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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Quantum computing in assistance to solve combinatorial optimization problems

2023 , Lorenz, Jeanette Miriam

Quantum computing as emerging technology is considered promising to provide more efficient or faster solutions to combinatorial optimization challenges. Such tasks appear in many different industrial settings, as e.g. in the logistics sector. However, in practice it turns out that a straight forward application of quantum algorithms to combinatorial optimization problems does not necessarily lead to a fast solution of good quality. Instead, the use of hybrid algorithms combining classical and quantum computing parts, or possibly quantum-inspired solutions, lead to more promising results. Taking concrete industrial application scenarios, this talk will discuss how potential quantum-assisted solutions for combinatorial optimization problems work, which challenges exist and which open points remain to be addressed in the future.

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A Comparative Study on Solving Optimization Problems with Exponentially Fewer Qubits

2024 , Winderl, David , Franco, Nicola , Lorenz, Jeanette Miriam

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.

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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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Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses

2023 , Winderl, David , Franco, Nicola , Lorenz, Jeanette Miriam

Leveraging 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 multi-class classification scenario. Consolidating our findings, we conducted experiments with a multi-class classifier adversarially trained on gate-based quantum simulators, further elucidating this unexpected behavior.

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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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Quantum-enhanced AI in medicine

2023 , Lorenz, Jeanette Miriam

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.

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QuaST - Quantum enabling Services and Tools for industrial applications

2023 , Lorenz, Jeanette Miriam

This talk presents progress on the QuaST project with respect to developing an additional abstraction layer for solving industrial optimization problems via quantum computing. Additionally, a quantum-assisted solution of a Capacitated Vehicle Routing Problem (CVRP) is presented.

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