Student-Abstracts-EN

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Assessing Noise Robustness of Variational Quantum Circuits in Reinforcement Learning Environments

Assessing Noise Robustness of Variational Quantum Circuits in Reinforcement Learning Environments

Abstract:

This bachelor thesis investigates the robustness of variational quantum circuits (VQCs) in reinforcement learning (RL) compared to classical neural networks under the influence of observation noise. Observation noise describes the uncertainty that arises when the states perceived by an RL agent deviate from the actual states of the environment, for example due to sensor noise, environmental influences or targeted adversarial attacks. A deterministic REINFORCE algorithm is used, which always selects the action with the highest probability prediction instead of the usual stochastic sampling. This methodological decision enables a targeted analysis of the direct influence of observation noise on the agent’s policy, independent of random exploration effects. Robustness is investigated using the deterministic variant of the well-known reinforcement learning environment Frozen-Lake, which is extended by an observation noise model with a self designed hot zone logic. Within these hot zones, the agent receives deliberately incorrect observations orthogonal to its original direction of movement. A classical neural network in form of a multi-layer perceptron (MLP) is compared with a VQC. Although the MLP often converges faster, it exhibits volatile and non-monotonic performance under increasing noise influence. In contrast, the VQC demonstrates superior stability with a predictable performance degradation, especially at higher noise levels. The results suggest that the structural properties of VQCs may enable better generalisation and robustness against structured observation noise.

Author:

Justin Dominik Marinus Klein

Advisors:

Julian Hager, Michael Kölle, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published July 2025 | Copyright © QAR-Lab
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Time Window-based Optimization of Communication Costs in Distributed Quantum Computing

Time Window-based Optimization of Communication Costs in Distributed Quantum Computing

Abstract:

This work develops and evaluates a two-stage optimization strategy that reduces communication costs in distributed quantum circuits. First, quantum circuits are modeled as undirected graphs and decomposed into two nearly equal-sized clusters using the Kernighan-Lin algorithm, which eliminates up to 60% of inter cluster CNOT edges. The remaining gates are divided into time windows. A heuristics-based allocation procedure prioritizes windows with maximum qubit overlap and even load distribution. This window structure reduces the simultaneous use of individual qubits and thus lowers the communication costs between execution units. The experiments on the Qiskit QASM simulator compare this method with a linear baseline in which the gates are processed sequentially and without partitioning. The study demonstrates that pairing graph partitioning with carefully tuned time window scheduling yields substantial savings while preserving logical correctness. Future work will target validation on physical hardware, integration of fault tolerant codes, and ML driven adaptive window sizing.

Author:

Rama Malhis

Advisors:

Leo Sünkel, Maximilian Zorn, Claudia Linnhoff-Popien

Student Thesis | Published June 2025 | Copyright © QAR-Lab
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Quantum Architecture Search for Solving Quantum Machine Learning Tasks

Quantum Architecture Search for Solving Quantum Machine Learning Tasks

Abstract:

Quantum computing is a computing paradigm based on the principles of quantum mechanics. This makes it fundamentally different from classical computing. For selected problem domains, quantum computers are expected to offer a performance advantage, the so-called quantum advantage, which manifests itself in exponentially faster computation times or lower resource requirements. In the current Noisy Intermediate Scale Quantum era, quantum hardware is still limited in performance and highly error-prone. Variational Quantum Circuits represent an approach that is comparatively robust to these limitations. The performance of these quantum circuits is highly dependent on the underlying architecture of the parameterized quantum circuit. The development of powerful, hardware-compatible circuit architectures is therefore an important task, also known as Quantum Architecture Search. Developing good architectures manually is an inefficient and error-prone process. First attempts have been made to automate this process. In addition to Evolutionary Algorithms, Differentiable Architecture Search, and Monte Carlo Tree Search, Reinforcement Learning is another potentially suitable approach for finding good architectures, but it has been relatively little studied. In particular, little is known about its suitability as a search strategy for Machine Learning problems. The goal of this work is to investigate Reinforcement Learning as a suitable search strategy for quantum circuits in the context of Machine Learning problems. For this purpose, the RL-QAS framework is presented, which enables the automated search for circuit architectures using a Reinforcement Learning Agent. The RL-QAS framework is evaluated on the Iris and binary MNIST classification problems. RL-QAS enabled the discovery of architectures that achieve high test accuracy in the classification of the aforementioned datasets while exhibiting low complexity. RL-QAS demonstrated that Reinforcement Learning is indeed suitable for architecture discovery. However, in order for RL QAS to be applied to more complex problems, further development of the approach is necessary.

Author:

Simon Salfer

Advisors:

Michael Kölle, Philipp Altmann, Claudia Linnhoff-Popien

Student Thesis | Published June 2025 | Copyright © QAR-Lab
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An Empirical Evaluation of Quantum Annealing-Based Image Classification Using Discriminative Quantum Boltzmann Machines

An Empirical Evaluation of Quantum Annealing-Based Image Classification Using Discriminative Quantum Boltzmann Machines

Abstract:

The Boltzmann machine has been highly influential in the development of artificial intelligence, serving as a foundational framework for energy-based models and neural network research. However, its direct applications in modern deep learning have been severely limited due to computational constraints. Classical sampling methods have consistently proven to be inefficient, rendering the processing of high-dimensional inputs practically infeasible. Therefore, alternatives like the Restricted Boltzmann Machine (RBM) have been introduced, sacrificing expressiveness for faster computations. In contrast, Quantum Boltzmann Machines can efficiently sample from approximate Boltzmann distributions when implemented using quantum algorithms such as quantum annealing. Empirical results suggest that this approach can yield a more efficient sampling process than classical methods, enabling more effective exploration of energy landscapes while reducing computational overhead. Additionally, this also makes full connectivity possible, preserving the expressiveness of the original BM. Nonetheless, to the best knowledge of the author, only a sparse amount of other studies have explored the capability of QBMs for supervised learning. This is particularly true for an application-driven context using real quantum hardware. Thus, the primary goal of this work is the evaluation of the practical effectiveness of QBMs utilizing discriminative learning for the classification of real-world image data using a novel embedding approach to save expensive Quantum Processing Unit time. This is done by employing discriminative QBMs, which always clamp the input units to a data point regardless of the current phase. The model can therefore learn the conditional distribution of a label given a data point. The results demonstrate competitive performance compared to discriminative BMs trained with simulated annealing and discriminative RBMs, while also indicating a slight reduction in the number of training epochs required. Additionally, the embedding approach proposed in this work significantly accelerated sampling, with an average speedup of 69.65% over the conventional embedding.

Author:

Mark Vorapong Seebode

Advisors:

Jonas Stein, Daniëlle Schuman, Claudia Linnhoff-Popien

Student Thesis | Published June 2025 | Copyright © QAR-Lab
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Quantum Transformers: Leveraging Variational Quantum Circuits for Natural Language Processing

Quantum Transformers: Leveraging Variational Quantum Circuits for Natural Language Processing

Abstract:

Recent advances in large language models (LLMs) have established transformer architectures as the dominant paradigm in natural language processing (NLP). While these models achieve state of the art performance, their exponential growth in parameter count and computational demands raises concerns regarding scalability, energy consumption and environmental impact. Simultaneously, quantum machine learning (QML) has emerged as a promising field that explores whether quantum computation can offer more efficient learning mechanisms, particularly using variational quantum circuits (VQCs), which have shown competitive performance with fewer parameters. This thesis investigates whether a quantum transformer model can be designed to structurally mirror the classical transformer while remaining feasible for execution on Noisy Intermediate-Scale Quantum (NISQ) hardware. To this end, we propose a modular, NISQ-compatible quantum transformer architecture that reproduces key classical components embedding, multi-head attention and encoder-decoder structure, using VQCs. Each component is implemented using shallow, strongly entangling circuits designed to minimize circuit depth and parameter count. The model is evaluated on synthetic language modeling tasks, comparing quantum and classical variants under matched conditions, including identical token vocabularies and equivalent parameter budgets. Results show that the quantum model is capable of learning simple formal languages, converging rapidly with fewer parameters and in some configurations achieving perfect reconstruction of deterministic token sequences. However, its performance degrades on more complex tasks requiring generalization, where classical models remain superior. These findings demonstrate the feasibility of the proposed quantum transformer architecture on near-term hardware and situate the model as a proof of concept for the architectural potential of encoder-decoder quantum transformers models in NLP.

Author:

Julian Hager

Advisors:

Michael Kölle, Gerhard Stenzel, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published June 2025 | Copyright © QAR-Lab
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Using Evolutionary Algorithms for Quantum Circuit Optimization under Noise

Using Evolutionary Algorithms for Quantum Circuit Optimization under Noise

Abstract:

Noise poses a prevalent challenge in the NISQ era of quantum computing. Its strong impact on the hardware of a quantum computer distorts the results of quantum circuits, especially with an increasing number of qubits and circuit depths. However, different circuit architectures that produce similar states can be exposed varying degrees of noise. This work presents an evolutionary algorithm aimed at finding an equivalent and less noisy circuit for a given quantum circuit. The algorithm’s fitness function evaluates the circuits based on their fidelity under noise compared to the noise-free state of the target circuit. With that, the evolutionary process is directed towards a noise-reduced solution. The results of the experiments show that the algorithm generally outperformed the randomly generated baseline and, in some cases, was able to find an optimized circuit compared to the target circuit. This demonstrates the potential of evolutionary algorithms for noise reduction. However, the scalability of the proposed evolutionary algorithm is severely limited.

Author:

Maria Trainer

Advisors:

Leo Sünkel, Maximilian Zorn, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published May 2025 | Copyright © QAR-Lab
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Emergent Cooperation in Quantum Multi-Agent Reinforcement Learning Using Communication

Emergent Cooperation in Quantum Multi-Agent Reinforcement Learning Using Communication

Abstract:

Emergent cooperation in classical Multi-Agent Reinforcement Learning has gained significant attention, particularly in the context of Sequential Social Dilemmas. While classical reinforcement learning approaches have demonstrated to be capable of emergent cooperation, research on extending these methods to the emerging field of Quantum Multi-Agent Reinforcement Learning remains limited, particularly through the usage of communication. In this work, we apply the two-phase communication protocol Mutual Acknowledgment Token Exchange (MATE), its extension Mutually Endorsed Distributed Incentive Acknowledgment Token Exchange (MEDIATE), the peer rewarding mechanism Gifting and Reinforced Inter-Agent Learning (RIAL), an approach to learn a discrete communication protocol, to quantum Q-Learning. We evaluate the resulting eight approaches in terms of their impact on emergent cooperation in three Sequential Social Dilemmas, namely the Iterated Prisoner’s Dilemma, the Iterated Stag Hunt and the Iterated Game of Chicken. Our experimental results show that the approaches MATETD, AutoMATE, MEDIATE-I and MEDIATE-S achieved high levels of cooperation across all three Sequential Social Dilemmas, demonstrating that communication is a viable method to achieve emergent cooperation in Quantum Multi-Agent Reinforcement Learning.

Author:

Christian Reff

Advisors:

Michael Kölle, Leo Sünkel, Claudia Linnhoff-Popien

Student Thesis | Published May 2025 | Copyright © QAR-Lab
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Analyzing the Parameter Adaption of Transfer Learning in Variational Quantum Eigensolvers

Analyzing the Parameter Adaption of Transfer Learning in Variational Quantum Eigensolvers

Abstract:

With the introduction of publicly available, yet noisy, Quantum Processors, many machine learning (ML) approaches have been proposed to make the most of the new capabilities. Peruzzo et al. proposed a hybrid algorithm, which implements a variational quantum eigensolver (VQE) to find the ground state of a Hamiltonian. While initially used in the field of quantum chemistry, VQEs can be used to solve a variety of optimization problems, such as finding a max-cut in a graph. As training is computationally expensive, transfer learning approaches have been proposed to reduce training time for similar problem instances. Rohe et al. introduce a VQE algorithm utilizing TL to speed up convergence in the max-cut problem. It was shown that TL is able to achieve convergence significantly faster in the early optimization phase, although training without TL yields slightly better results over time. However, when training time is drastically reduced, TL is able to produce good results while drastically reducing the computational cost of training. Furthermore, it was shown that the similarity of the optimal solution correlated positively with the success of TL. The similarity was measured by calculating the minimal hamming distance (HD) between the VQE’s solution of the source graph and the optimal solutions of the target graph. This thesis will be based primarily on the work done by Rohe et al. Specifically, the aim of the thesis is to analyze the quality of the parameter transfer to solve max-cut graph problems. Thus, instead of trying to demonstrate the applicability of TL for the VQE, it will be investigated where TL causes the algorithm to over- or under-adapt and how these results come about. The source-and target-graphs are sampled form the publicly available California street network as well as Facebook social circle data. Here the source graph will be utilized to train parameters which are to be transferred to initialize the training of the target graph. To evaluate the similarity of the source- and target-graph applied to the max-cut problem, the optimal max-cut solutions are calculated via brute force. Afterward the minimal HD between optimal solutions of the source and target-graphs are calculated. As TL might not always find one of the optimal solutions, the HD between the source solution and the target solution found through TL are calculated. This will provide information about whether TL caused the VQE to over- or under-adapt. As the quality of trained solutions appears to deteriorate as the HD between source- and target-graph solutions increase, it is of high interest to find ways to handle these kinds of problems. A possible explanation for over- or under-adaption is that the pre-trained parameters trap the VQE in a local optimum, inhibiting further exploration of the solution landscape. Through the analysis of the influence TL has on the training process of the VQE as well as under- and over-adaption, this thesis aims to better evaluate the role and quality of parameter transfer in the NISQ era.

Author:

Julio Amaru Nicolas Brocca Alvarado

Advisors:

Tobias Rohe, Sebastian Woelkert, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published April 2025 | Copyright © QAR-Lab
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Exploring Entanglement-intensity in Variational Quantum Eigensolver Algorithms for Combinatorial Optimization

Exploring Entanglement-intensity in Variational Quantum Eigensolver Algorithms for Combinatorial Optimization

Abstract:

Variational Quantum Algorithms (VQAs), including the Quantum Approximate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE), and Quantum Neural Networks (QNNs), have emerged as promising approaches in the noisy intermediate-scale quantum (NISQ) era. These hybrid quantum-classical algorithms aim to solve optimization and simulation problems under the constraints of limited qubit connectivity, gate errors, and decoherence. A central feature of quantum computing, and a distinguishing factor from classical methods, is entanglement—the quantum correlation between qubits that enables certain computational advantages. While entanglement is widely considered essential for the success of VQAs, recent studies have challenged the assumption that more entanglement always improves algorithmic performance. Instead, excessive entanglement can introduce barren plateaus, increase optimization difficulty, and degrade convergence.
This work investigates the role of entanglement in the performance of the VQE, a leading algorithm for approximating ground-state energies of quantum Hamiltonians. Specifically, it explores whether limiting entanglement through structured reductions improves trainability and solution quality. To systematically analyze this relationship, two entanglement manipulation strategies are employed: (1) Dropout-based entanglement sparsification, where entangling gates are randomly removed based on a given probability, and (2) Parameterized entanglement tuning, where the strength of controlled entangling operations is constrained by a variable rotation parameter. The impact of these strategies is evaluated across three circuit ansätze by evaluating convergence behaviour as well as measuring three key-metrics: entangling capability, expressibility and approximation ratio. The results reveal that reducing entanglement via dropout improves optimization dynamics by potentially mitigating barren plateaus and increasing gradient variance, leading to faster convergence and lower final energies without compromising solution quality. However, the varying responses across different ansätze suggest that entanglement reduction should be tailored to circuit topology and problem structure rather than applied uniformly. In contrast, parameterized entanglement tuning shows a weaker influence on both trainability and final solution quality, particularly in deeper circuits where cumulative entanglement compensates for local gate-level adjustments. Notably, the study finds that convergence behavior serves as a more reliable indicator of VQE performance than expressibility or entangling capability alone, emphasizing that entanglement should be actively managed rather than maximized indiscriminately.

Autor/in:

Joel Friedrich

Betreuer:

Tobias Rohe, Philipp Altmann, Thomas Gabor, Claudia Linnhoff-Popien

Studentische Abschlussarbeit | Veröffentlicht April 2025 | Copyright © QAR-Lab
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Determining links in product data using Quantum Restricted Boltzmann Machines

Determining links in product data using Quantum Restricted Boltzmann Machines

Abstract:

The increasing share of software in products not only drives innovation but also increases complexity. To minimize the risk of malfunctions in software-intensive products and ensure traceability, links between development stages and production data are necessary. These are mandated by regulations such as ISO/IEC 15288 and DIN/ISO 26262. The Digital Data Package standard enables the management of such links. However, implicit links currently have to be created manually, which leads to challenges due to the scope and frequent product changes. A promising approach for the automatic identification of links is the use of classifiers. In particular, Quantum Restricted Boltzmann Machines offer a viable solution due to the limited availability of linked development data and their high susceptibility to noise. For evaluation, classical neural networks and pre-trained classifiers are used. As established methods in pattern recognition, they serve as a baseline for assessing new classifiers.

Author:

Simon Hehnen

Advisors:

Michael Kölle, Jonas Stein, Dr. Fabrice Mogo Nem (PROSTEP AG), Claudia Linnhoff-Popien

Student Thesis | Published April 2025 | Copyright © QAR-Lab
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