Student-Abstracts-EN

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Quantum-Enhanced Denoising DiffusionModels

Quantum-Enhanced Denoising Diffusion Models

Abstract:

Machine learning models for generating images have gained much notoriety in the past year. DALL-E, Craiyon and Stable Diffusion can generate high-resolution images, by users simply typing a short description (prompt) of the desired image. Another growing field is quantum computing, particularly quantum-enhanced machine learning. Quantum computers solve problems using their unique quantum mechanical properties. In this paper we investigate how the use of Quantum-enhanced Machine Learning and Variational Quantum Circuits can improve image generation by diffusion-based models. The two major weaknesses of classical diffusion models are addressed, the low sampling speed
and the high number of required parameters. Implementations of a quantum-enhanced denoising diffusion model will be presented, and their performance is compared with that of classical models, by training the models on well-known datasets (MNIST digits and fashion, CIFAR10). We show, that our models deliver better performance (measured in FID, SSIM and PSNR) than the classical models with comparable number of parameters.

Author:

Gerhard Stenzel

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Jonas Stein, Andreas Sedlmeier

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Dimensionality Reduction with Autoencodersfor Efficient Classification with VariationalQuantum Circuits

Dimensionality Reduction with Autoencoders for Efficient Classification with Variational Quantum Circuits

Abstract:

Quantum computing promises performance advantages, especially for data-intensive and complex computations. However, we are currently in the Noisy Intermediate-Scale Quantum era with a limited number of qubits available, which makes it challenging to realize these potential quantum advantages in machine learning. Several solutions, like hybrid transfer learning have been proposed, whereby a pre-trained classical neural network acts as the feature extractor and a variational quantum circuit as the classifier. While these approaches often yield good performance, it is not possible to clearly determine the contribution of the classical and quantum part. The goal of this thesis is therefore to introduce a hybrid model that addresses these limitations and implements a clear distinction between the classical and quantum parts. An autoencoder is used to reduce the input dimension. We compare the performance of transfer learning models (Dressed Quantum Circuit and SEQUENT) and a variational quantum circuit with amplitude embedding against our model. Additionally, the performance of a purely classical neural network on the uncompressed input and an autoencoder in combination with a neural network will be examined. We compare the test accuracies of the models over the datasets Banknote
Authentication, Breast Cancer Wisconsin, MNIST and AudioMNIST. The results show that the classical neural networks and the hybrid transfer learning approaches perform better than our model, which matches our expectations that the classical part in transfer learning plays the major role in the overall performance. Compared to a variational quantum circuit with amplitude embedding, no significant dierence can be observed, so that our model is a reasonable alternative to this.

Author:

Jonas Maurer

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Philipp Altmann, Leo Sünkel

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Approximating Quadratic Unconstrained Binary Optimization Problems using Graph Convolutional Neural Networks

Approximating Quadratic Unconstrained Binary Optimization Problems using Graph Convolutional Neural Networks

Abstract:

The quantum annealing hardware currently available has not yet reached the stage to successfully compete with ecient heuristics on classical machines, due to limitations in size and connectivity. Confronted with this challenge, the approach to approximate QUBO matrices by removing certain entries before solving them on the quantum hardware has been introduced. This is done to reduce the size and the complexity of the embedding, anticipating benefits with regard to the size of the solvable problems as well as the quality of the solutions.
We will extend this approach by using artificial neural networks to generate suitable approximations based on the structure of the matrix. The proposed model consists of two separate networks, a graph convolutional neural network to compute features for the nodes in the QUBO graph and a second fully connected network to derive a decision, whether the connection between two nodes should be removed from the matrix. A genetic algorithm was employed to train the model, using instances of seven dierent problems. Problem specific phase transitions were taken into account to confront the model with
easy and hard problem instances.
The trained models were subsequently evaluated using classical and quantum solvers, comparing the performance of the approximated matrix with the original matrix, another approximation strategy and classical approaches. The experiments provided satisfying results for certain problems, as the approximated matrices were partially able to produce even better results than the original matrices. In other respects, it became apparent, that this approach is not applicable to all problems.

Author:

Felix Ferdinand Mindt

Advisors:

Claudia Linnhoff-Popien, David Bucher, Sebastian Zielinski

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Application of graph partitioning algorithms and genetic algorithms to optimize teleportation costs in distributed quantum circuits.

Application of graph partitioning algorithms and genetic algorithms to optimize teleportation costs in distributed quantum circuits.

Abstract:

Currently, we are in the Noisy Intermediate Scale Quantum (NISQ) era, where the number of qubits that can be used in a single quantum computer is increasing. However, with this development come challenges in handling large quantum systems. Distributed quantum computation is therefore gaining importance to overcome these challenges. In this process, multiple quantum computers or quantum processing units are connected to work together on a problem. This enables the use of larger computational capacities and more efficient solutions to complex tasks. In distributed quantum computing, different units or subsystems communicate with each other to exchange quantum information. The basic teleportation protocol plays an important role in this process. It enables the transfer of quantum information between subsystems. An important aspect is to minimize the number of teleportations. Thus, the aim is to increase the accuracy of quantum computations, reduce the error-proneness of qubits, and at the same time make resource consumption more efficient.In this work, different graph partitioning algorithms, such as the Kernighan-Lin algorithm and spectral partitioning, a genetic algorithm (GA), and two hybrid genetic algorithms (HGA), which are a combination of the graph partitioning algorithms and a GA, are applied and investigated to minimize the number of global quantum gates and the associated teleportation costs. First, the graph partitioning algorithms are used to partition the nodes as uniformly as possible. In addition, a GA is implemented to take care of the partitioning of qubits using random partitions. The two HGAs lead to a near-optimal arrangement of the global quantum gates after the qubits are partitioned using the graph partitioning algorithms. Finally, the proposed approaches are investigated using nine benchmark circuits and compared in terms of the number of global quantum gates and teleportation costs. Random searches are also performed for the GA and the two HGAs to verify their performance with respect to the optimization objective. The results indicate a significant improvement in teleportation cost.

Author:

Teodor Slaveykov

Advisors:

Leo Sünkel Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published August 2023 | Copyright © QAR-Lab
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NISQ-ready community detection on weighted graphs using separation-node identification

NISQ-ready community detection on weighted graphs using separation-node identification

Abstract:

An important optimization problem in computer science is the detection of communities. By analyzing networks, so-called communities can be found and important information in many fields – from biology to social structures – can be derived. By weighting individual edges, even more information can be processed than by the mere presence of these edges. However, for community detection on weighted graphs, more factors must be considered as a result. Since this is an NP-hard optimization problem, heuristics are often used to find an acceptable solution faster and more efficiently. One promising approach is the use of quantum computers, as it has already been experimentally shown that they can achieve more efficient results than classical computers in certain domains (e.g., Grover or Shor algorithm). However, since most approaches to community detection using QUBO matrices consume a lot of memory, the goal of this work is to find an approach with a good memory efficiency. To this end, this work presents a promising community detection approach based on the detection and analysis of separation nodes, which has the advantage that the dimensions of the resulting QUBO matrix do not exceed the number of nodes and the matrix itself is as sparse as the adjacency matrix of the graph. These separating nodes are designed to divide the graph when they are removed such that the remaining components are each exactly part of a community. This approach is extended to weighted graphs by determining the probability that an edge is a separating edge based on the information flow of the neighborhood. This approach is tested using synthesized graphs with a fixed ground truth about their communities, to which weights are assigned without changing the community structure.

Translated with www.DeepL.com/Translator (free version)

Author:

Dominik Ott

Advisors:

Jonas Stein, Jonas Nüßlein, Claudia Linnhoff-Popien

Student Thesis | Published August 2023 | Copyright © QAR-Lab
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Influence of Embedding-Methods on the Generalization of Quantum Machine Learning

Influence of Embedding-Methods on the Generalization of Quantum Machine Learning

Abstract:

Quantum Machine Learning is a promising field of application for quantum computers. However, to see real advantages over classical computers, advanced quantum fundamentals are needed. One of the building blocks of quantum computers are embeddings, which convert real data into quantum data. In this work, the focus is on the influence of various embedding methods on the ”quality” of a Quantum Machine Learning model. As the focus is on these embeddings, the model and quantum circuit are kept simple. They solve a binary classification problem. Nevertheless, the interplay of certain embeddings with different circuits is also of interest and is briefly discussed in this work. Since much already exists in the literature about the embedding methods ”Angle Embedding” and ”Amplitude Embedding”, this work also focuses on other embedding methods from the literature. To determine the quality of a model, we examined its generalizability. For this, we used various metrics from classical Machine Learning. Although the question of the best embedding could not be answered, interesting insights were gained about the effects of the embeddings on different datasets.

Author:

Steffen Brandenburg

Advisors:

Einfluss von Embedding Methoden auf Generalisierbarkeit in Quantum Machine Learning

Leo Sünkel, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published August 2023 | Copyright © QAR-Lab
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Quantum-Multi-Agent-Reinforcement-Learning mit Evolutionärer Optimierung (en)

Title

Abstract:

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Author:

Max Mustermann

Advisors:

Claudia Linnhoff-Popien

Student Thesis | Published {Month YYYY} | Copyright © QAR-Lab
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Anomaly Detection using Quantum Circuit Born Machines (en)

Anomaly Detection using Quantum Circuit Born Machines

Abstract:

Anomaly detection is a critical component in various fields, including finance, medical diagnosis, and fraud detection. As datasets become increasingly complex and larger, traditional computers face limitations in processing power. In contrast, quantum computers oer promising solutions through the physical properties of their qubits, such as entanglement and superposition. The emergence of quantum machine learning, particularly the quantum circuit born machines (QCBMs), is introduced as a promising approach to tackle such complex problems. QCBMs are parameterized quantum circuits that can be trained to generate samples from a target distribution. The goal of this work is to leverage this ability for detecting anomalies that have a distribution dierent from that of normal data points. The effectiveness of QCBMs for anomaly detection is explored using a dataset generated by the make_blobs method from the Scikit-learn package in Python, where some outliers can be clearly distinguished from the clusters. And its performance is compared with an autoencoder model using the ROC-curve and the Matthews correlation coecient (MCC). These metrics are used to evaluate the models’ ability to detect anomalies and avoid false positives. The results show that QCBMs outperform the autoencoder when trained with a smaller dataset, indicating that QCBMs are more eective in dealing with data and can learn the underlying distribution more eciently than the autoencoder. However, both models can learn the distribution when trained with the full dataset.

Author:

Ahmad Almohamad Alissa

Advisors:

Jonas Stein, Danielle Schumann, Claudia Linnhoff-Popien

Student Thesis | Published April 2023 | Copyright © QAR-Lab
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Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs (en)

Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs

Abstract:

Quantum walks, a quantum analog of classical random walks, have emerged as a powerful paradigm in quantum computation and simulation. While classical random walks rely on stochastic processes to explore systems, quantum walks leverage the unique properties of quantum mechanics to perform these tasks more efficiently. In particular, discrete-time quantum walks (DTQWs) have been studied extensively for their applications in graph theory, such as graph isomorphism, graph connectivity, and graph-based search problems. Despite their potential, implementing DTQWs on near-term quantum devices remains challenging. While previous works have focused on quantum circuit implementations for DTQWs with uniform coin operators, implementing non-homogeneous coin sets is a complex task that requires new approaches. This thesis presents an efficient quantum circuit architecture for implementing coined DTQWs with non-homogeneous, position-dependent coin sets on a large subset of bipartite graphs. A novel edge labeling scheme, Gray Code Directed Edges encoding, is introduced, taking advantage of Gray code for position encoding and the bipartite structure of the underlying graph to minimize the complexity of the quantum circuits representing coin and shift operators. This optimization leads to fewer gate operations, reducing the impact of noise and errors in near-term quantum devices. A labeling scheme is developed for various graph topologies, including cycle graphs, chained cylinder graphs, and square grid graphs, which are especially relevant for reinforcement learning applications. These findings offer a new perspective on the implementation of coined quantum walks and lay a foundation for future research on quantum walks with non-homogeneous coin sets.

Author:

Viktoryia Patapovich

Advisors:

Jonas Stein, Michael Kölle, Maximilian-Balthasar Mansky, Claudia Linnhoff-Popien

Student Thesis | Published July 2023 | Copyright © QAR-Lab
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Analyzing Reinforcement Learning strategies from a parameterized quantum walker (en)

Analyzing Reinforcement Learning strategies from a parameterized quantum walker

Abstract:

Reinforcement Learning has made significant progress in solving complex problems. Hence, it is not surprising that it can be found in various application domains. Quantum Computing as well is a prospering field, where big advancements could be seen over the last decades. Better quantum computers led to first experimentally proven quantum supremacy. Hence, the field of research grew which led to improvements in various application domains of quantum computing, one of them being quantum Reinforcement Learning where quantum computing is combined with classical reinforcement learning techniques. Among other approaches, quantum walks are used as quantum computational framework which is also the case in the present work. Here, the approach of using parameterized coin matrices to determine the behaviour of the walker adapted to grid graphs is used. Thereby, the parameters of the coin matrices should be learned, such that an optimized performance of the walker to perform a specific task is reached. In this thesis the feasibility of this approach applied to a grid world is investigated using grids of the size 2×2 and 4×4. Furthermore, a new concept for including additional constraints by introducing an extra environment qubit is presented and its influence on the optimization process of the parameters examined. The results can be seen as a proof of concept as for all experiments the approach used here shows better results than the random baseline. Moreover, no negative influence of the environment qubit can be detected. The results gained here are a basis for further research using this approach.

Author:

Lorena Wemmer

Advisors:

Jonas Stein, Michael Kölle, Claudia Linnhoff-Popien

Student Thesis | Published May 2023 | Copyright © QAR-Lab
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