Basket Option Pricing with Quantum Circuits
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Tobias RoheType: Bachelor thesisCompleted on: April 15, 2026
The valuation of basket options poses a complex numerical challenge due to their dependence on multiple underlying assets and their correlations. While classical Monte Carlo methods require substantial computational effort as the dimensionality increases, machine learning approaches enable a direct approximation of the pricing function. The objective of this thesis is to investigate variational quantum circuits (VQCs) for approximating basket option prices and to compare their performance with established classical neural network architectures. The training data are generated using Monte Carlo simulations whose parameters are estimated from historical market data. Different payoff structures (Worst-of, Best-of, and Average) are considered, and the effects of training dataset size, artificial noise, and a temporally ordered train–test split are analyzed. In addition, the frequency structure of the target functions is examined using a Non-Uniform Fast Fourier Transform in order to relate the representational capacity of the VQCs to the spectral properties of the pricing function. The results show that both classical neural networks and VQC-based models can approximate the pricing function with high accuracy. While classical networks tend to benefit from increasing model size, VQCs achieve most of their maximum performance already at moderate circuit depth, which is consistent with the predominantly low-frequency structure of the target functions. Under limited data availability and strong noise, simpler models prove to be more robust, whereas more complex architectures only reach their full potential when sufficient training data are available. Overall, VQC-based models achieve a competitive approximation performance, although they do not demonstrate a clear advantage over classical neural networks in the investigated setting.
Optimizing Parameterized Quantum Hamiltonians via Implicit Differentiation
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Tobias Rohe, Jonas SteinType: Master thesisCompleted on: April 15, 2026
Variational quantum algorithms are among the most promising approaches for solving combinatorial optimization problems on near-term quantum hardware. A practically relevant but so far underexplored case are parameterized Hamiltonians in which the problem structure itself~-- such as the edge weights of a Max-Cut instance~-- depends on an external control parameter. Such dependencies arise naturally when calibration settings, design variables, or physical constraints influence the problem instance. Jointly optimizing control and circuit parameters gives rise to a bilevel problem. This makes the overall procedure inherently expensive, since even a single outer optimization step requires a full inner solve. Existing derivative-free methods aggravate this issue, as they require multiple outer-function evaluations per step~-- each of which triggers its own full inner solve~-- and thus multiply the already high cost of the bilevel procedure. This thesis introduces Correlator-Reuse Implicit Differentiation (CR-ID), an approach that avoids this overhead: at inner optimality, the outer gradient can be expressed as a weighted sum of edge-cut probabilities that are already obtained during energy evaluation. The outer optimization step therefore requires no additional inner solves and the overall procedure converges significantly faster. Additionally, the thesis introduces a benchmark family that systematically separates scale from functional shape in the edge weights, and an analysis of how the algorithm architecture affects the exactness of this gradient. Eight experiments under matched budgets show that CR-ID consistently improves budget-normalized performance over derivative-free baselines~-- across difficulty levels, graph classes, readout models, and high-dimensional control. The architecture study further reveals a practical advantage of VQE over QAOA at the expectation level, while QAOA can partially recover this gap at the final readout stage. The results demonstrate that implicit differentiation with correlator reuse substantially accelerates bilevel quantum optimization of parameterized Max-Cut problems without requiring additional circuit evaluations.
Impact of Different Quantum Noise Channels on Global Model Convergence and Robustness in Quantum Federated Learning
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Leo Sünkel, Tobias RoheType: Bachelor thesisCompleted on: March 30, 2026
This bachelor thesis investigates the potential of \textit{Quantum Federated Learning} (QFL) as a decentralized training architecture for medical image processing in the NISQ era. The focus is on the challenge of developing a robust global model based on parameterized quantum circuits, while local client systems are influenced by both data heterogeneity and physical quantum noise. First, the thesis evaluates to what extent the use of QFL can reduce the negative impact of an \textbf{uneven class distribution} (\textit{Label Distribution Skew}) within a hospital network. The results demonstrate that QFL significantly reduces local bias severity and effectively closes the performance gap between majority and minority classes (\textit{Performance Gap}) compared to purely local models. Furthermore, the research question addresses how different noise models -- namely \textit{Bit-Flip}, \textit{Phase-Flip}, \textit{Depolarization}, and \textit{Amplitude Damping} as well as \textit{Phase Damping} -- influence the training dynamics and generalization capability of the global model. In a simulated environment for pneumonia detection, it is quantitatively proven that the system exhibits high robustness against Pauli errors, while the amplitude damping channel represents a critical barrier to convergence at an error probability of $p=0.10$. However, the study confirms an inherent resilience of the federated network against hardware outliers, as malfunctions of individual, highly noisy clients are compensated for by global aggregation. Thus, this work provides important insights into the stability and practical feasibility of quantum algorithms in unreliable, heterogeneous networks.
Dataset-Based Comparative Analysis of Quantum Advantage in Quantum Reservoir Computing
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Thomas Gabor, Maximilian ZornType: Master thesisCompleted on: March 30, 2026
Quantum reservoir computing (QRC) has emerged as a promising framework for leveraging the rich nonlinear dynamics of quantum systems to perform machine learning tasks with reduced training overhead. This work presents a dataset-based investigation into gate-based QRC, benchmarking it against established classical random mapping architectures: the echo state network for dynamic tasks and the extreme learning machine for static tasks. While classical models maintain a performance lead in traditional benchmarks such as the Mackey-Glass time series, our results demonstrate a considerable quantum advantage in native quantum domains. In a Unitary Regression task, the QRC model outperformed the classical baseline while utilizing 92% fewer readout parameters and achieving a 300-fold increase in training speed. Investigations into architectural congruency further reveal a measurable performance hierarchy, showing that QRC efficiency is profoundly enhanced by structural similarities between the reservoir and the target system. Furthermore, our analysis of hybrid interpolation tasks identifies a critical crossover point where classical architectures face an expressive bottleneck when approximating quantum complexity. These findings suggest that the structural inductive bias and high feature density of quantum reservoirs provide a measurable advantage for quantum-native applications, establishing a foundation for future hardware-executed QRC paradigms in the noisy intermediate-scale quantum era.
Systematic Evaluation of Reservoir Usage in Quantum Reservoir Computing
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Thomas Gabor, Maximilian ZornType: Master thesisCompleted on: March 30, 2026
Reservoir computing is motivated by the idea that useful temporal processing can emerge from fixed recurrent dynamics, yet in quantum reservoir computing this claim is often difficult to isolate from preprocessing and downstream readout effects. This thesis therefore introduces a unified evaluation protocol for testing that claim in QRC rather than inferring it indirectly from end-to-end benchmark scores. The first axis tests whether recurrent dynamics add value beyond matched static baselines when preprocessing and readout conditions are controlled. The second axis uses readout probes and knowledge distillation to examine what remains readable in frozen recurrent states and how far the recurrent mapping can be replaced by compact static students. Within this framework, the thesis addresses the sequential NISQ dilemma through the proposed Leaky-Recurrent Quantum Reservoir Computing (LR-QRC) architecture, a gradient-free restarting-based model that feeds back a compressed measurement-derived memory state while keeping the quantum core fixed. The recurrent channel scales with local observables rather than full probability-vector feedback and remains compatible with shallow gate-based execution. The third evaluation axis then uses symmetrically tuned chaotic forecasting benchmarks to test memory, stability, and hardware-conscious efficiency under logical-depth and feedback-scaling constraints. Along the first axis, row-sequential MNIST serves as the main controlled benchmark and shows that recurrent dynamics contribute beyond preprocessing and downstream readout capacity. Along the second axis, readout probes and distillation show that the frozen LR-QRC states remain strongly readable by fixed second-order readouts even though the recurrent input-to-state mapping is only partially reproducible by compact static students. Along the third axis, Lorenz 63 and Mackey–Glass serve as memory and efficiency stress tests; tuned classical LI-ESN baselines remain stronger overall, revealing a clear remaining long-memory gap. At the same time, under a conservative mixed-depth comparison, LR-QRC is the best-performing gate-based baseline among the compared models on Lorenz 63. These results support a narrow conclusion: recurrent dynamics in QRC can add measurable value beyond matched static baselines, and LR-QRC provides a stronger and more hardware-conscious gradient-free recurrent baseline than several prior gate-based QRC models, even though strong classical reservoirs remain superior overall.
Constraint-guided Robotic Handover with Reinforcement Learning
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Maximilian Zorn, Philipp AltmannType: Bachelor thesisCompleted on: March 30, 2026
A Study on Classical and Quantum Contributions in Hybrid Quantum Transfer Learning
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Leo Sünkel, Julian SchoenbergerType: Bachelor thesisCompleted on: March 27, 2026
While hybrid quantum-classical models hold significant potential for advancing machine learning, their practical impact on real-world tasks such as image classification depends on several critical factors. This study specifically investigates the classical and quantum contributions in Hybrid Quantum Transfer Learning, examining whether integrating a quantum component can enhance efficiency and performance compared to fully classical models. To achieve this, this study focuses on hybrid quantum-classical machine learning, where classical neural networks act as feature extractors and parametrized quantum circuits serve as adaptive classifiers. However, current quantum hardware limitations, including restricted circuit depth and constraints on qubit quantity, place boundaries on the effectiveness of quantum components. Experiments were conducted using a classical model, a classical control model, and a hybrid quantum-classical model, evaluated on two datasets: the Modified National Institute of Standards and Technology (MNIST) dataset and a reduced subset of the Canadian Institute for Advanced Research 10-class (CIFAR-10) dataset. Results illustrate that hybrid quantum models are capable of learning, but remain unable to surpass classical models in performance accuracy under current quantum resource limitations. The classical feature extractor remained the main contributor to model performance, whereas the quantum component primarily functioned as an additional transformation layer, providing only minimal efficiency gains. Together, these findings highlight the current constraints of hybrid quantum transfer learning, indicating that prioritizing improvements in quantum hardware, training approaches, and circuit configuration is essential to enable its practical integration and future development.
Curriculum Reinforcement Learning for Drone Navigation in Confined 3D-Environments
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Maximilian Zorn, Philipp AltmannType: Bachelor thesisCompleted on: March 27, 2026
The autonomous navigation of micro quadrotors in complex, unmapped indoor spaces requires robust and reactive control strategies. This thesis develops an agent based on Reinforcement Learning that navigates relying exclusively on a single-channel egocentric depth image and local kinematic data. To address the challenges of partial observability and sparse rewards, two sequence modeling approaches (Frame Stacking and LSTM) are compared. Additionally, an adaptive Curriculum Learning strategy is combined with extensive Domain Randomization. The results demonstrate that Frame Stacking offers superior reactivity and sample efficiency for agile avoidance maneuvers, whereas the LSTM architecture ensures greater flight stability, particularly regarding yaw control. Furthermore, the structured curriculum proves essential for mastering complex topological challenges such as lateral S-curves, enabling the agent to successfully generalize its learned policy to unseen, procedurally generated environments.
Assessing Adversarial Robustness of Variational Quantum Circuits in Reinforcement Learning
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Julian Hager, Michael KölleType: Bachelor thesisCompleted on: March 27, 2026
Adversarial attacks pose a significant threat to the reliability of intelligent systems, particularly in safety-critical domains where small, targeted actions can lead to severe performance degradation. Although the vulnerability of classical deep reinforcement learning agents to such attacks has been widely studied, the robustness of quantum reinforcement learning models remains largely unexplored. Recent work suggests that Quantum Reinforcement Learning methods, and in particular, agents based on Variational Quantum Circuits (VQCs), may offer inherent robustness against certain classes of noise due to quantum architectural properties, raising the question of whether these resilience properties also transfer to adversarial manipulation. In this work, we empirically investigate the adversarial robustness of VQC-based reinforcement learning agents. We compare VQC agents to classical neural network policies trained using the same evolutionary optimization procedure and evaluate both architectures on the CartPole-v1 and LunarLander-v3 environments. To assess robustness, we implement several observation-space attacks of increasing sophistication, including constant perturbations, random noise, a black-box policy-induction attack, and a learned adversarial network. Agent performance is evaluated under these perturbations and compared across attack scenarios. Our results provide an empirical assessment of how variational quantum policies behave under targeted adversarial conditions and investigate whether the noise-tolerant nature of VQCs translates into improved robustness in reinforcement learning settings.
Kolmogorov-Arnold Networks for Continuous Thought Machines
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Julian Hager, Gerhard StenzelType: Bachelor thesisCompleted on: March 27, 2026
In this bachelor thesis we try to examine the effect of exchanging the Multilayer Perceptron Learner (MLP) Neuron Level Model (NLM) of Sakana AI's recent research on Continuous Thought Machines (CTM) with a Kolmogorov-Arnold Network (KAN), which we think suits the motivation behind introducing CTMs more properly. The main idea of Continuous Thought Machines is to improve classical machine learning models in terms of their original biological role model: the human brain. Generally speaking, human brains operate fundamentally differently compared to MLPs. Since neuroscience discovered that neuron activity is % look up neuro science actually linking neuron firing activity, we can argue that classical MLPs, which although seem to still deliver promising performances, are an overly simplistic modeling of the real human brain, merely focusing on their output values. Continuous Thought Machines aim to mimic human brains by introducing a time domain and by self-synchronizing neuron activity in Neural Networks. Our hypothesis is that with its wave-shaped activation functions, KAN Networks used in CTMs can perform better on tasks that the classical CTM still struggles on. In this thesis we try to find out which learning patterns on the CTM with KAN occur, how it performs compared to the normal CTM and more typical machine learning models like Recurrent Neural Networks or ResNets on tasks such as QAMNIST, CIFAR-10 and ListOps. We came to the conclusion, that the KAN is suitable as a NLM. Despite being more expensive in computation, the KAN can outperform the MLP on selected tasks with reasonable additional expense.
Individual Encodings for Self-Adaptive Recombination in Evolutionary Algorithms
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Thomas Gabor, Maximilian ZornType: Bachelor thesisCompleted on: March 18, 2026
This bachelor thesis examines whether recombination in evolutionary algorithms can be controlled by adding individually encoded markers and whether such self-adaptive mechanisms provide optimization performance advantages over static crossover baselines. While recombination can be beneficial, its e!ectiveness is highly problem-dependent: an operator that performs well on one benchmark may be ine!ective on another, and operator utility can also change across di!erent phases of a run. To address this, we implement three marker-based self-adaptive variants—Spears bit, float marker, and revised float marker, where each individual carries an additional marker that influences which crossover operator is applied during reproduction. We compare these approaches against three static baselines: fixed uniform, fixed two-point, and a 50/50 fixed random choice, which keep their operator usage constant throughout the run. All variants share the same evolutionary loop and di!er only in the mechanism used to select the crossover operator. We evaluate the algorithms on common benchmark problems, including continuous minimization functions and binary maximization benchmarks with building-block structure (HIFF and Royal Road). Optimization performance is measured via the best objective value per generation over 50 independent runs, and adaptive behavior is analyzed through realized operator usage and marker trajectories. The results show that self-adaptive algorithms reliably shift recombination usage depending on the benchmark used. However, under our configuration, self-adaptive variants do not consistently outperform the strongest static baselines across all domains. On most continuous functions, self-adaptive variants reduce two-point usage, indicating adaptation toward uniform crossover, whereas on the binary building-block benchmarks they increase two-point usage, consistent with the advantage of preserving contiguous blocks. Overall, individual-level encodings yield interpretable operator shifts, while their impact on final optimization performance remains benchmark- and configuration-dependent.
LLMs as Mutation and Recombination Operators in Evolutionary Algorithms
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Thomas Gabor, Maximilian ZornType: Bachelor thesisCompleted on: March 18, 2026
This thesis investigates the use of a general-purpose large language model, Meta Llama 3.2 (3B parameters), as a mutation operator within an evolutionary algorithm. The optimization tasks considered were the Rastrigin problem and the Factory Robot Route problem. LLM-based mutation was statistically compared to conventional random number generator (RNG)-based mutation with respect to mutation strength, mutation biases introduced by the LLM, and overall mutation performance. Both English and German prompts were evaluated. The results indicate that LLM-based mutation produces excessively large modifications, with the English prompt leading to larger changes than the German prompt. In addition, several systematic biases were identified, including a preference for discrete mutation steps, discrete gene values, mutations of the first gene, mutations without actual change, sign-related tendencies, and repeated generation of specific numbers. These biases were considerably weaker for the English prompt.\\In terms of performance, LLM-based mutation underperformed RNG-based mutation in all evaluated scenarios. We hypothesize that this is primarily caused by an excessive degree of change rather than by the identified biases. This assumption is supported by the observation that the English prompt, which exhibited fewer biases but larger mutation changes, performed worse than the German prompt.\\Finally, we examined whether explicitly instructing the LLM within the prompt to avoid certain biases could mitigate them. The findings suggest that such mitigation is difficult to control. It produces the opposite effect in some cases and often leads to unintended side effects. Furthermore, affirmative phrasing proved slightly more effective than the use of negations. However, since Mutation Impact appears to be the primary limiting factor---and can be controlled through post-generation validation of LLM-generated individuals---we consider LLM-based mutation a promising direction for future research. Moreover, for complex data types such as text or source code, LLMs currently represent one of the few practical mutation mechanisms available.
Evaluation of Optimization Factors in Quantum Algorithms for Train Rerouting
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Maximilian Zorn, Jonas SteinType: Bachelor thesisCompleted on: March 16, 2026
This work investigates two hybrid quantum algorithms for solving the train (re)routing problem: quantum annealing with QUBO formulation on D-Wave hardware and the quantum approximate optimization algorithm (QAOA+) with admissibility-preserving mixers on IBM gate model quantum computers. Both approaches are integrated into a Benders decomposition, where the combinatorial master problem is solved by quantum hardware and the admissibility is verified by a classical SMT solver.Systematic ablation studies are used to analyze the influence of various hyperparameters on solution quality. For quantum annealing, longer annealing times (100~$\mu$s), moderate chain strength values (2.0–4.0), and low constraint penalty weights prove to be advantageous. The QAOA+ approach shows a non-monotonic relationship between circuit depth and solution quality, with even low depths ($p=1$ to $p=3$) achieving competitive results. The evaluation is performed on three datasets of real timetable data with 7 to 14 trains. While quantum annealing with optimal configuration shows deviations of 110% to 317% compared to the exact Gurobi solver, the QAOA+ approach achieves an interesting result. On the normal data set, it outperforms both the greedy heuristic and the exact solver by 13.4%. This result demonstrates that quantum algorithms can already beat classical methods under certain problem constellations. The paper offers specific configuration recommendations for both approaches and discusses the practical implications for using quantum optimization in railroad planning.
Privacy-Preserving Training of Quantum Circuits via Homomorphic Encryption
Supervision: Claudia Linnhoff-Popien, Thomas Gabor, Gerhard Stenzel, Michael KölleType: Master thesisCompleted on: March 11, 2026
Access to quantum hardware is currently limited to a small number of cloud providers, requiring organisations to transmit data to remote servers to execute algorithms on physical devices; Quantum Homomorphic Encryption (QHE) enables computations directly on encrypted quantum states, but existing schemes supporting universal gate sets either require extensive client–server interaction for each non-Clifford gate or demand a large number of auxiliary qubits far beyond the capacity of present-day NISQ devices, leaving no practical privacy-preserving method for training parametrised quantum circuits; here we develop a protocol based on the Pauli one-time pad with a key-dependent sign adaptation of circuit weights that enables the training of parametrised quantum circuits on encrypted states, formalise it as a cryptographic protocol, and prove its correctness, while requiring neither per-gate interaction, nor quantum capabilities on the client beyond state preparation, nor auxiliary qubits; information leakage is quantified using two complementary approaches, namely an algebraic analysis based on the rank of the key expansion matrix over $\mathbb{F}_2$ bounding static leakage from a single observation and a statistical analysis using hidden Markov models capturing dynamic leakage across the full training trajectory; the circuit architecture directly influences security and maximal security is achieved only when generators depend on all components of the encryption key; overall, the proposed protocol provides a lightweight alternative to formally secure but resource-intensive QHE schemes and opens a practical path toward privacy-preserving quantum cloud computing in the NISQ era.
Mathematical reasoning in small language models: Comparing challenges and potentials of different prompting strategies
Author: Patrik FelbingerSupervision: Philipp Altmann, Thomas Gabor, Thomas Gabor, Claudia Linnhoff-PopienType: Master thesisCompleted on: January 14, 2026
Empirical Evaluation of Quantum Circuit Ansatz Design Effects for Supervised Learning
Author: Alexander KovacsSupervision: Michael Poppel, Jonas Stein, Thomas Gabor, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: January 14, 2026
Ingredient Recognition and Relative Quantity Estimation in Food Images on Hardware-Constrained Systems
Author: Michael AnderleSupervision: Gerhard Stenzel, Michael Kölle, Thomas Gabor, Claudia Linnhoff-PopienType: Master thesisCompleted on: December 3, 2025
A Comparison of the Ant Colony Algorithm and Dijkstra’s Algorithm for Routing in Quantum Networks
Author: Felix MichlSupervision: Leo Sünkel, Tobias Rohe, Thomas Gabor, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: December 3, 2025
Generalization in a Natural-Language-Based Genetic Algorithm
Author: Sarah GernerSupervision: Thomas Gabor, Gerhard Stenzel, Thomas Gabor, Claudia Linnhoff-PopienType: Master thesisCompleted on: November 12, 2025
A Comparison of Echo State Networks and Spiking Neural Networks for Reservoir Computing
Author: Flo HelmbergerSupervision: Philipp Altmann, Thomas Gabor, Thomas Gabor, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: November 12, 2025
Improving Cooperative MARL through Curriculum Learning for Dynamic Role Assignment
Author: David EngelSupervision: Maximilian Zorn, Philipp Altmann, Thomas Gabor, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: November 12, 2025
Exploring the Practical Application of Quantum-Native Self-Attention for Quantum Vision Transformers
Author: Joel FurtakSupervision: Jonas Stein, Michael Kölle, Claudia Linnhoff-PopienType: Master thesisCompleted on: November 12, 2025
Vision Transformers (ViTs) have emerged as a powerful alternative to convolutional neural networks in computer vision, demonstrating superior performance across numerous tasks due to their ability to capture global relationships through the self-attention mechanism. Unlike previously established methods that focus primarily on local features, ViTs process images by analysing relationships between patches, allowing for flexible architectures that excel at modelling global dependencies. Despite their success, the self-attention mechanism in ViTs faces computational challenges when deployed in resource-constrained environments or real-time applications where efficiency is paramount. This limitation has motivated the exploration of different approaches using quantum computing, thatpreserve the global modelling capabilities of ViTs while reducing computational overhead within the self-attention mechanism. While some approaches aim to replicate the self-attention mechanism using trainable compound matrices, this thesis proposes a Quantum Vision Transformer (QViT) architecture native to the quantum paradigm, that leverages the Quantum Singular Value Transformation (QSVT) to approximate the self-attention mechanism. The proposed model integrates parameterized quantum circuits (PQCs) to encode patch-wise image embeddings, employs a Linear Combination of Unitaries (LCU) to mix patch representations in an attention-like manner, and applies the QSVT to introduce non-linear expressivity. In addition, a quantum classification circuit extends the data register with trainable class qubits, which serve as a quantum analogue to the classical class token and are measured to obtain the final outputs. To assess the models’ capability in image classification tasks, it is evaluated on Bars-and-Stripes and binary MNIST datasets, where it achieves up to∼99% accuracy. An analysis of the models’ computational complexity shows improved theoretical scaling with input size, as well as lower parameter counts. The results obtained in this thesis serve as proof-of-concept for the proposed QViT model and its application to computer vision tasks.
Offline Quantum Reinforcement Learning using Metaheuristic Optimization Strategies
Author: Frederik BickelSupervision: Michael Kölle, Julian Hager, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: October 8, 2025
This thesis investigates offline quantum reinforcement learning (QRL) with variational quantum circuits (VQCs) and metaheuristic optimization. O!ine reinforcement learning (RL) provides a realistic training paradigm in which agents learn entirely from fixed datasets instead of online interaction, making it particularly suited for reproducible studies and controlled comparisons. For the offline training, we created a dataset for the CartPole-v1 environment by combining random, medium, and expert policies, resulting in 525,000 transitions with diverse state–action coverage. On this dataset, we evaluated the effectiveness of four gradient-free metaheuristic optimizers: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Tabu Search (TS). We trained a DQN agent with a 4-qubit, 2-layer VQC. Their performance is compared to a gradient-based gradient descent (GD) baseline with Adam optimizer. Each optimizer undergoes per-factor hyperparameter tuning, followed by an optimizer comparison on a single dataset pass.
Geometric Quantum GANs: Topology-Driven Architectures for Graph Generation
Supervision: Tobias Rohe, Claudia Linnhoff-PopienCompleted on: October 1, 2025
The generative modeling of complexly structured data, such as graphs with embedded geometric constraints, continues to represent a fundamental challenge for classical machine learning approaches. In this study, we investigate the potential of Quantum Generative Adversarial Networks (QuGANs) to overcome these limitations by focusing on a representative benchmark task: the generation of complete graphs with four nodes (K4) that reflect plausible flight routes/topologies. These graphs must satisfy important geometric properties to be considered physically valid within Euclidean space, particularly the triangle inequality for all sub-triangles and the Ptolemaic inequality for each four-node pair. We present a rigorous comparative analysis between a classical Generative Adversarial Network (GAN) and several hybrid QuGAN variants, each using a different quantum generator architecture. These include a generic and a problem-oriented entangled approach that directly incorporates the structural priors of the target graphs into the design of the quantum circuit.
Evolutionary Optimization of Variational Quantum Circuits for High Accuracy with Minimal Parameterized Gates
Author: Tobias DaakeSupervision: Leo Sünkel, Maximilian Zorn, Thomas Gabor, Claudia Linnhoff-PopienType: Bachelor thesisCompleted on: September 17, 2025
Variational Quantum Circuits (VQCs) represent one of the most promising approaches for leveraging the capabilities of near-term quantum computers. While they offer a high degree of flexibility and adaptability, VQCs face significant challenges, particularly with respect to trainability and scalability. To address these limitations, this work explores the use of evolutionary algorithms for the automatic generation of VQCs with a minimal number of parameterized gates. This approach enables a systematic investigation of the role such gates play in the optimization of VQCs for common benchmark problems.The proposed method is evaluated in the context of a classification task, with particular attention to classification accuracy and the number of parameterized gates required. Experiments were conducted on random circuits with 4 and 6 qubits with variable circuit depth. The results demonstrate that reducing the number of parameters improves the optimization process, leading to classifiers that exhibit greater robustness and enhanced accuracy.