Student-Abstracts-EN

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Towards Less Greedy Quantum Coalition Structure Generation in Induced Subgraph Games

Towards Less Greedy Quantum Coalition Structure Generation in Induced Subgraph Games

Abstract:

Switching to 100 % renewable energy production is one of the most important steps societies are currently taking in combating the climate crisis. This switch however requires new techniques for the management of power networks, such as their division into micro-grids containing sensible subsets of prosumers. Creating this division in an optimal manner is a challenging optimization problem which can be simplified to the Coalition Structure Generation problem in Induced Subgraph Games. This is a problem formulation in which one seeks to divide an undirected, fully-connected, weighted graph into a set of fully-connected subgraphs, in a manner that maximizes the sum over the weights of the edges contained in these subgraphs. In the last few years, several Quantum Annealing (QA)-based approaches have been proposed to solve this problem, the most recent of which is an efficient, but greedy algorithm called GCS-Q. In this thesis, we propose many different, less greedy QA-based approaches to solving the above-mentioned problem, to see if any of these algorithms can outperform GCS-Q in terms of solution quality. Testing these approaches on three different solvers – the QBSolv software, the D-Wave Advantage 4.1 quantum annealer and the QAOA algorithm using qiskit’s simulation software – we find that, while none of our suggested approaches can outperform the quantum state- of-the-art algorithm on current QA hardware, most of them do when using the QBSolv software. The best of these approaches is an algorithm we call 4-split iterative R-QUBO, which finds the optimum for all problem graphs in our dataset and scales quite favorably with the graph size in terms of runtime. Thus, we see this algorithm as a promising candidate for future research on quantum approaches for the problem in question.

Author:

Daniëlle Schuman

Advisors:

Jonas Nüßlein, David Bucher, Claudia Linnhoff-Popien

Student Thesis | Published May 2024 | Copyright © QAR-Lab
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Evaluating Metaheuristic Optimization Methods for Quantum Reinforcement Learning

Evaluating Metaheuristic Optimization Methods for Quantum Reinforcement Learning

Abstract:

Quantum Reinforcement Learning offers the potential for advantages over classical Reinforcement Learning, such as a more compact representation of the state space through quantum states. Furthermore, theoretical studies suggest that Quantum Reinforcement Learning can exhibit faster convergence than classical approaches in certain scenarios. However, further research is needed to validate the actual benefits of Quantum Reinforcement Learning in practical applications. This technology also faces challenges such as a flat solution landscape, characterized by missing or low gradients, which makes the application of traditional, gradient-based optimization methods inefficient. In this context, it is necessary to examine gradient-free algorithms as an alternative. The present work focuses on the integration of metaheuristic optimization algorithms such as Particle Swarm Optimization, Ant Colony Optimization, Tabu Search, Simulated Annealing, and Harmony Search into Quantum Reinforcement Learning. These algorithms offer flexibility and efficiency in parameter optimization, as they utilize specialized search strategies and adaptability. The approaches are evaluated within two Reinforcement Learning environments and compared to random action selection. The results show that in the MiniGrid environment, all algorithms lead to acceptable or even very good results, with Simulated Annealing and Particle Swarm Optimization achieving the best performance. In the Cart Pole environment, Simulated Annealing and Particle Swarm Optimization achieve optimal results, while Ant Colony Optimization, Tabu Search, and Harmony Search perform only slightly better than an algorithm with random action selection. These results demonstrate the potential of metaheuristic optimization methods such as Particle Swarm Optimization and Simulated Annealing for efficient learning in Quantum Reinforcement Learning systems, but also highlight the need for careful selection and adaptation of the algorithm to the specific problem.

Author:

Daniel Seidl

Advisors:

Michael Kölle, Maximilian Zorn, Claudia Linnhoff-Popien

Student Thesis | Published May 2024 | Copyright © QAR-Lab
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Finding Arbitrage with different Quantum Algorithms

Finding Arbitrage with different Quantum Algorithms

Abstract:

Quantum computing, a discipline that leverages the principles of quantum physics to perform complex calculations, has emerged as a transformative field since its initial conceptualization by Richard Feynman and Yuri Manin in the 1980s. Recent advancements in quantum hardware, coupled with a surge in investment, have accelerated the application of quantum computing across a diverse range of sectors with one of them being finance. Financial operations often boil down to combinatoric optimization problems, which makes them are well suited to quantum methods. Specifically, this work focuses on identifying optimal arbitrage opportunities in financial markets, such as currency exchange. Arbitrage can be framed as a combinatorial optimization problem, solvable through quantum annealing or quantum gate-based computing methods.
Building on the foundation laid by Gili Rosenberg, this work explores the efficacy of quantum annealing and conducts comprehensive benchmarks against other quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA). Also a novel oracle encoding enhanced by Quantum Fourier Transformation (QFT) to solve the arbitrage problem using Grover’s algorithm is introduced. Recognizing that the number of qubits and the size of the quantum circuit are among today’s major computational bottlenecks, recently established pre-processing and post-processing techniques are employed to optimize computational efficiency across the various quantum algorithms studied.

(This research was produced in cooperation with Aqarios GmbH)

Author:

Jakob Anton Mayer

Advisors:

Jonas Nüßlein, Jonas Stein, Nico Kraus, Claudia Linnhoff-Popien

Student Thesis | Published March 2024 | Copyright © QAR-Lab
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Optimization of Variational Quantum Circuits for Hybrid Quantum Proximal Policy Optimization Algorithms

Optimization of Variational Quantum Circuits for Hybrid Quantum Proximal Policy Optimization Algorithms

Abstract:

Quantum computers, which are subject to current research, offer, apart from the hope for an quantum advantage, the chance of reducing the number of used trainable parameters. This is especially interesting for machine learning, since it could lead to a faster learning process and lower the use of computational resources. In the current Noisy Intermediate-Scale Quantum (NISQ) era the limited number of qubits and quantum noise make learning a difficult task. Therefore the research focuses on Variational Quantum Circuits (VQCs) which are hybrid algorithms constructed of a parameterised quantum circuit with classic optimization and only need few qubits to learn. Literature of the recent years proposes some interesting approaches to solve reinforcement learning problems using the VQC, which utilize promising strategies to increase its results that deserve closer research. In this work we will investigate data re-uploading, input and output scaling and an exponentially declining learning rate for the actor-VQC of a quantum proximal policy optimization (QPPO) algorithm, in the Frozen Lake and Cart Pole environments, on their ability to reduce the parameters of the VQC in relation to its performance. Our results show an increase of hyperparameter stability and performance for data re-uploading and our exponentially declining learning rate. While input scaling has no effect on the parameter effectiveness, output scaling can archive powerful greediness control and lead to a rise in learning speed and robustness.

Author:

Timo Witter

Advisors:

Michael Kölle, Philipp Altmann, Claudia Linnhoff-Popien

Student Thesis | Published February 2024 | Copyright © QAR-Lab
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Path-Connectedness of the Boundary between Features that Are Labeled Differently by a Single Layer Perceptron

Path-Connectedness of the Boundary between Features that Are Labeled Differently by a Single Layer Perceptron

Abstract:

Due to the remarkable advancements in high-performance computing, machines can process an increasingly high amount of data to adjust numerous parameters in a Machine Learning model (ML model). In this way, the machine recognizes and learns patterns and might come to good and fast decisions. Though, the success of an ML model does not just depend on the performance of the computer where it is deployed on that assures the capability of processing huge databases. Mostly, a high amount of data is helpful, but not the key to obtain a reliable model itself. Already models with just a few trainable parameters, where smaller data sets are sufficient for the training, can produce stunning outputs if the basic model is chosen adequately and fits to the data and to the task.

From an abstract point of view, ML models are parameterized functions, where the parameters are optimized during the learning process. To examine if a certain ML model qualitatively fits, we can set up requirements in a mathematical way. Here, we discuss specifications that do not consider a concrete assignment of the parameters but expect a certain behavior of the to a model corresponding function for arbitrary parameters. Subsequently, we can prove that a certain model fulfills them, or give a more specific counter-example, which yields that a certain mathematical property does not hold, in general, for the regarded model.

In this thesis, we consider a Single Layer Perceptron (SLP), the root of Deep Neural Networks, that categorizes features between two different labels. We show that under certain preconditions the boundary between the two categories within the feature space is path-connected. This indicates the SLP being a proper choice if we have pre-knowledge about the features: If we know that the boundary between the two categories is path-connected in reality, we can exclude such models that generate a boundary with gaps.

Author:

Remo Kötter

Advisors:

Maximilian Balthasar Mansky, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published December 2023 | Copyright © QAR-Lab
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Construction of quantum circuits with restricted gates

Construction of quantum circuits with restricted gates

Abstract:

In practice, a quantum computer, like a classical computer, has only a limited set of operations. These operations, called quantum gates, are modelled by unitary transformations according to the postulates of quantum mechanics. As opposed to classical circuits, so-called qubits are manipulated. However, implementing such a system is challenging, leading to the applicability of only selected quantum gates. In order to execute an arbitrary circuit on a quantum computer, the implemented basic set must be able to generate any unitary transformation. In this thesis, we will present a characterisation of so-called exact universal sets for systems with up to two qubits and specify a necessary set of properties for an arbitrary number of qubits. Quantum gates for single qubits can be equated to three-dimensional rotations, so that two non-parallel axes of rotations are sufficient. Larger systems, however, require non-local gates that can replace the rotations of individual qubits (local gates). Through a recursive decomposition, we will construct an exact universal set for any number of qubits and demonstrate the necessary properties. The results provide insight into the design of basic operations needed to generate any transformation. Finally, this work aims to provide an approach to identify sufficient properties of exact universal sets of any number of qubits to uniquely characterize them. This open problem could increase the efficiency of decomposing given quantum gates and eliminate unnecessary elements.

Author:

Sebastian Wölckert

Advisors:

Maximilian Balthasar Mansky, Sebastian Zielinski, Claudia Linnhoff-Popien

Student Thesis | Published January 2024 | Copyright © QAR-Lab
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Efficient semi-supervised quantum anomaly detection using one-class support vector machines

Efficient semi-supervised quantum anomaly detection using one-class support vector machines

Abstract:

Quantum computing is an emerging technology that can potentially improve different tasks in machine learning. Combining the representational power of a classically hard quantum kernel and the one-class SVM, a noticeable improvement in average precision can be achieved compared to the classical version. However, the usual method of calculating these kernels comes with a quadratic time complexity in terms of data size. To address this issue, we try two different methods. The first consists of measuring the quantum kernel using randomized measurements, while the second one uses the variable subsampling ensemble method to achieve linear time complexity. Our experiments show that both of these methods reduce the training times by up to 95% and inference times by up to 25%. While the methods lead to lower performance, the average precision is slightly better than the classical RBF kernel.

Author:

Afrae Ahouzi

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Pascal Debus, Dr. Robert Müller

Student Thesis | Published November 2023 | Copyright © QAR-Lab
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Using Quantum Machine Learning to Predict Asset Prices in Financial Markets

Using Quantum Machine Learning to Predict Asset Prices in Financial Markets

Abstract:

In the financial world, a lot of effort is spent on predicting future asset prices. Gaining even a modest increase in forecasting capability can generate enormous profits. Some statistical models identify patterns, trends, and correlations in past prices, and apply those patterns to forecast future values. A more novel approach is the use of artificial intelligence to learn underlying trends in the data and predict future prices. As quantum computing matures, its potential applications in this task have also become increasingly more interesting. In this thesis, several different models of these various types are implemented: ARIMA, RBM, LSTM, and QDBM (Quantum Deep Boltzmann Machine). These models are trained on historical asset prices and used to predict future asset prices. The model predictions are then also used as the input for a simulated trading algorithm, which investigates the effectiveness of these predictions in the active trading of assets. The predictions are performed for ten different assets listed on the NYSE, NASDAQ, and XETRA, for the five-year period from 2018 to 2022. The assets were chosen from varying industrial sectors and with diverse price histories. Trading based on the model predictions was able to either match or outperform the classic buy-and-hold approach in nine out of the ten assets tested.

Author:

Maximilian Adler

Advisors:

Claudia Linnhoff-Popien, Jonas Stein, Jonas Nüßlein, Nico Kraus (Aqarios GmbH)

Student Thesis | Published November 2023 | Copyright © QAR-Lab
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A Reinforcement Learning Environment for directed Quantum Circuit Synthesis

A Reinforcement Learning Environment for directed Quantum Circuit Synthesis

Abstract:

Fueled by recent advances in quantum computing technologies, the design of optimized quantum circuits including reliable quantum state preparation are topics gaining more and more importance. Common approaches often require a high amount of Know-How and manual calculation hampering implementation, especially if the involved circuits increase in qubit number and gate count. Hence, addressing the rise in possible gate-to- qubit combinations by utilizing machine learning techniques represents a promising step in the development of the field. The following study aims to provide a reinforcement learning environment enabling the training of agents on the directed quantum-circuit design for the preparation of quantum states. Thus, the trained agents are enabled to create quantum circuits facilitating the preparation of desired target states, which can be handed over as inputs. In the course of this, all generated quantum-circuits are built utilizing gates from the Clifford+T gate set only. Based on the implemented environment, we conducted experiments to investigate the relation between the depth of the reconstructed quantum circuits and the involved target state parameters. The explored parameter-space included the respective qubit number and circuit-depth used for the target initialization. By providing a division of the parameter-space into several difficulty regions and a collection of well-known states, we facilitated benchmarking of different reinforcement learning algorithms on the quantum-circuit synthesis problem. Specific findings of the study include the generation of PPO-algorithm-based agents, which outperform the random-baseline. Through the application of the trained agents on the benchmarking tests we show their ability to reliably design minimal quantum-circuits for a selection of 2-qubit Bell states.

Author:

Tom Schubert

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Philipp Altmann

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