Student-Abstracts-EN

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Emerging Cooperation through Quantum Entanglement in Multi-Agent Systems

Emerging Cooperation through Quantum Entanglement in Multi-Agent Systems

Abstract:

This thesis investigates the feasibility of quantum entanglement enhancing cooperation in multi-agent reinforcement learning. Utilizing the iterated prisoner dilemma as a benchmark, we propose a decentralized multi-agent reinforcement learning framework where two MARL agents equipped with variational quantum circuits can affect each other through quantum entanglement. Unlike existing approaches that rely on dedicated quantum communication channels, this thesis examines whether entanglement alone can facilitate cooperative equilibria. Therefore, we evaluate the effects of different entanglement architectures to develop mutual cooperative strategies that escape the Nash equilibrium. The results of our experiments indicate that while entanglement can facilitate strategies that outperform the defection baseline, long-term cooperative behavior remains unfeasible, suggesting that quantum correlations alone are insufficient to sustain cooperative strategies in multi-agent reinforcement learning settings.

Author:

Marvin Heinrich

Advisors:

Michael Kölle, Leo Sünkel, Claudia Linnhoff-Popien

Student Thesis | Published March 2025 | Copyright © QAR-Lab
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Distributed Quantum Machine Learning -Training and Evaluating a Machine Learning Model on a Distributed Quantum Computing Simulator

Distributed Quantum Machine Learning -Training and Evaluating a Machine Learning Model on a Distributed Quantum Computing Simulator

Abstract:

The training and execution of machine learning models on quantum hardware is typically limited by the number of available qubits. A potential approach to overcoming this limitation is Distributed Quantum Machine Learning (DQML), where models are partitioned and executed across multiple quantum computers. While this increases the number of available qubits and potentially enables the training of larger models, it also introduces substantial classical and quantum communication overhead, leading to increased computational costs and extended training times. To investigate this approach and its limitations, this thesis presents a DQML model using a classical server and two quantum clients, implemented with the distributed quantum framework NetQASM. We evaluated the model on datasets with two and four features using a quantum network simulator and it achieved classification performance comparable to that of a centralized quantum baseline. To address the communication overhead, which resulted in training times of 50 to 500 minutes per epoch, optimizations in circuit design, entanglement generation, and distributed gate execution were implemented and evaluated. These adaptations led to a reduction in runtime of up to 60% while maintaining competitive classification accuracy.

Author:

Kian Izadi

Advisors:

Leo Sünkel, Michael Kölle, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published March 2025 | Copyright © QAR-Lab
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QUBO-Generation for (MAX-)3SAT via generative AI-Methods

QUBO-Generation for (MAX-)3SAT via generative AI-Methods

Abstract:

Creating QUBOs for 3-SAT formulas using pattern QUBOs poses several challenges. Generating pattern QUBOs and building the QUBO structure itself is technically demanding due to the brute-force approach. In this study, two machine-learning approaches for QUBO generation given a 3-SAT formula are tested. Various encoding methods were explored for representing formulas and matrices. Formula encodings included vector, Word2Vec, and BERT-based methods, while latent representations were tested on QUBOs. As an initial model, a conditional autoencoder was used, with variations like dual encoders and pretrained encoders based on a RESNET18 architecture also evaluated. Accurate QUBOs could be generated for formulas with a single clause, but for formulas with up to four clauses, energy levels of solution and non-solution states overlapped. Finally, a conditional diffusion model was implemented and trained on 5 and 7 clause random formulas using vector, Word2Vec, and BERT formula embeddings. QUBOs generated with BERT formula embeddings fulfilled the highest average number of clauses per formula, though most formulas remained unsolved. Training with masked diffusion further improved performance, as QUBOs generated with masking fulfilled, on average, one additional clause. However, this approach requires a predefined mask during data generation. The sparse QUBO data structure and challenges in encoding 3-SAT formulas are likely primary factors behind these results.

Author:

Philippe Wehr

Advisors:

Sebastian Zielinski, Michael Kölle, Claudia Linnhoff-Popien

Student Thesis | Published March 2025 | Copyright © QAR-Lab
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Space-Efficient Quantum Optimization for the Traveling Salesman Problem via Binary Encoding of Feasible Solutions

Space-Efficient Quantum Optimization for the Traveling Salesman Problem via Binary Encoding of Feasible Solutions

Abstract:

The Traveling Salesperson Problem (TSP) is a classic combinatorial optimization problem with multiple applications in logistics, planning, and scheduling. Quantum algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA), have demonstrated potential for addressing such NP-hard problems and potentially can offer advantages over classical methods. Existing quantum approaches to the TSP typically rely on one-hot encoded states, requiring O(n^2) qubits for a TSP instance with n cities and using constraint-preserving mixers like the XY-mixer to navigate the feasible subspace. However, these methods are resource-intensive and face scalability issues due to the large number of qubits needed. This master thesis investigates a novel, space-efficient encoding scheme for solving the TSP using QAOA with a binary encoding of permutations, reducing the qubit requirement to O(n log2 n). The main challenge of binary encoding is the absence of an simple constraint-preserving mixer to maintain feasibility during optimization. To address this, an efficiently implementable unitary transformation was proposed to assign each binary-encoded tour a unique label. By adding O(log2 n!) ancillary qubits that represent each possible permutation of the TSP in factorial-base system, a canonical isomorphism between permutations and factorial-base numbers is established. The mixing operation is then performed on this ancillary space through a simpler X-mixer or a Grover mixer, automatically restricting the algorithm’s evolution to valid tours. This ensures that hard constraints remain satisfied throughout the optimization process, enabling faster convergence toward the optimal solution. Three variants of this encoding are explored in this master thesis: (1) a direct unitary transformation using a precomputed look-up table, (2) a quantum arithmetic–based method, and (3) an index-only approach that encodes both cost and mixer Hamiltonians in [log2(n!)] qubits, potentially introducing higher-order interactions. Numerical experiments with small problem instances demonstrate the feasibility of these approaches, highlighting the prospective benefits of this space-efficient encoding scheme in practical quantum optimization tasks.

Author:

Viktoria Patapovich

Advisors:

Jonas Stein, David Bucher, Claudia Linnhoff-Popien

Student Thesis | Published January 2025 | Copyright © QAR-Lab
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Minimizing Teleportation and Enhancing Fidelity in Distributed Quantum Computing using a Multi-Objective Evolutionary Algorithm

Minimizing Teleportation and Enhancing Fidelity in Distributed Quantum Computing using a Multi-Objective Evolutionary Algorithm

Abstract:

Quantum computing is considered a promising technology for solving tasks that are impossible even for classical computing. However, individual quantum computers are reaching their limits due to various challenges and can therefore only provide a limited number of freely available qubits. This limitation can be overcome by implementing the distributed quantum computing (DQC), a concept that increases the number of available qubits by connecting multiple quantum computers via a quantum network. Within such a system qubits are transferred from one quantum computer to another using quantum teleportation, a resource-intensive but indispensable protocol for communication in the DQC. Minimizing the number of teleportation is therefore essential, but carries the risk of affecting the functionality of the circuit when removing global gates that rely on teleportation. To overcome these challenges this paper presents an multi-objective evolutionary algorithm (EA) that leverages mechanisms such as crossover, mutation and selection to minimize the number of quantum teleportations while maximizing fidelity, which is a measure of similarity. The EA was tested on a set of QFT benchmark circuits and random circuits to evaluate its effectiveness in solving the problem. The results demonstrate that the evolutionary algorithm can significantly reduce the number of teleportations while maintaining fidelity above the threshold of 0.9. In comparison to the Kernighan-Lin-Algorithm, which only provides local optima, this approach consistently achieves better results.

Author:

Abasin Omerzai

Advisors:

Leo Sünkel, Thomas Gabor, Michael Kölle, Claudia Linnhoff-Popien

Student Thesis | Published January 2025 | Copyright © QAR-Lab
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Evaluating Parameter-Based Training Performance of Neural Networks and Variational Quantum Circuits

Evaluating Parameter-Based Training Performance of Neural Networks and Variational Quantum Circuits

Abstract:

In recent years, neural networks (NN) have played a central role in significant advancements in the field of machine learning. The increasing complexity of machine learning tasks leads to NNs with a growing number of trainable parameters, resulting in high computational and energy demands. Variational quantum circuits (VQC) are a promising alternative. They leverage quantum mechanics to model complex relationships and tend to require fewer trainable parameters compared to NNs. In this work, we evaluate and compare the training performance of NNs and VQCs on simple supervised learning and reinforcement learning tasks, considering multiple models with varying numbers of parameters. The experiments with VQCs are conducted using a simulator. To approximate how long training the VQCs would take using currently available real quantum hardware, selected parts of the training process are executed using a real quantum computer. Our results confirm that VQCs can achieve performance comparable to NNs while requiring significantly fewer parameters. Despite longer training times, our findings suggest that VQCs could be advantageous for certain machine learning tasks, particularly as quantum technology continues to rapidly advance, algorithms are optimized, and VQC architectures are improved.

Author:

Alexander Feist

Advisors:

Michael Kölle, Jonas Stein, Claudia Linnhoff-Popien

Student Thesis | Published January 2025 | Copyright © QAR-Lab
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Leveraging Preconditioning to Speed Up Quantum Simulation-Based Optimization

Leveraging Preconditioning to Speed Up Quantum Simulation-Based Optimization

Abstract:

Simulation-based optimization is computationally intensive requiring many evaluations of complex simulations to optimize an objective function. Quantum algorithms can provide a better runtime over classical methods by simultaneously evaluating multiple possible solutions. If the objective function and/or constraints depend on the summary statistic information derived from the result of a simulation, the problem is classified as a Quantum Simulation-Based Optimization (QuSO) problem. A subclass of QuSO is LinQuSO, where the simulation component can be formulated as a system of linear equations. The calculation of the objective function depends on the complexity of solving the corresponding linear system of equations, which is linear influenced by the condition number of the system. A recent paper introduced a quantum algorithm for solving prototypical second-order linear elliptic partial differential equations, which are discretized by 𝑑-linear finite elements on Cartesian grids within a bounded 𝑑-dimensional domain. By using a BPX preconditioner the system of linear equations is transformed into a well-conditioned one. Functionals of the solution can be computed for a given tolerance 𝜀 with a complexity of 𝒪(︀polylog (︀𝜀−1)︀)︀ and a quantum advantage over classical solvers is accomplished for 𝑑 > 1. This work shows how to improve the efficiency of computing optimal input parameters for a LinQuSO problem by inserting the preconditioning algorithm into the Quantum Approximate Optimization Algorithm (QAOA), which results in a runtime of 𝒪(︀𝜀−1 polylog (︀𝜀−1)︀)︀ for the simulation component. The new approach is demonstrated with an example of a topology optimization problem for heat conduction.

Author:

Carlotta von L’Estocq

Advisors:

Jonas Stein, David Bucher, Claudia Linnhoff-Popien

Student Thesis | Published January 2025 | Copyright © QAR-Lab
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Warm Starting Variational Quantum Algorithms for Parameterized Combinatorial Optimization

Warm Starting Variational Quantum Algorithms for Parameterized Combinatorial Optimization

Abstract:

In the Noisy Intermediate Scale era of Quantum Computing (NISQ), Variational Quantum Algorithms (VQAs) are a key paradigm for producing useful results in spite of hardware limitations. These algorithms can be adapted to multiple domains, such as condensed matter physics and combinatorial optimization. Problems in these domains can be modeled as Ising Hamiltonians. To model physical systems, Hamiltonians usually contain parameters controlling global forces, such as magnetic fields. In contrast, Hamiltonians modeling combinatorial optimization problems (COPs) are usually not parametrized in the literature, describing a specific problem instance. However, in reality, multiple global variables, such as the time of the day or the direction of the market, can influence instances of COPs. This thesis introduces parametrized Hamiltonians for combinatorial optimization through the Maximum-Cut and Knapsack problems, presenting a framework that can be extended to other COPs. The framework widens current approaches for modeling COPs to describe multiple problem instances using a single Hamiltonian with global parameters. Subsequently, this work investigates the optimization of parametrized COPs using various variants of VQAs, testing alternative objective functions tailored specifically for COPs. Finally, this work investigates the transfer of optimized parameters between problem instances corresponding to different Hamiltonian parameter values, evaluating whether parameters producing satisfactory solutions for one configuration of a problem can produce similar results for different configurations. Two simple modifications to existing techniques are presented for this task, termed Adaptive Start and Aggregated Learning. This thesis presents a different approach to combinatorial optimization and investigates the potential of this new framework.

Author:

Federico Harjes Ruiloba

Advisors:

Tobias Rohe, Jonas Stein, Claudia Linnhoff-Popien

Student Thesis | Published December 2024 | Copyright © QAR-Lab
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Circuit Partitioning and Genetic Optimization for Efficient Qubit Distribution in Distributed Quantum Computing

Circuit Partitioning and Genetic Optimization for Efficient Qubit Distribution in Distributed Quantum Computing

Abstract:

Quantum computers are capable of solving specific computational problems in a time frame that is faster than that of a classical computer. The current era is that of Noisy Intermediate-Scale Quantum Computing, which is defined by the presence of noise that limits the capabilities of quantum computation. This presents a significant challenge in the development of large-scale quantum computers. The encoding of problems is accomplished through the use of quantum circuits comprising qubits. The distribution of qubits across quantum computers may facilitate the execution of larger circuits. In Distributed Quantum Computing, qubits are distributed across multiple Quantum Processing Units, which are connected via a quantum network. Alternatively, large quantum circuits can be run using circuit partitioning, which reduces depth and allows for parallel execution. However, partitioning a circuit might not take the constraints of the network into account. A method for integrating network constraints into the distribution process is through the use of an evolutionary algorithm. This approach has been employed to improve the distribution of qubits on a quantum network, albeit to a limited extent. The objective of this study is to consider the distinctive characteristics of a network and, moreover, the particular costs associated with each operation. To evaluate the efficiency of our algorithm, we conducted experiments on two distinct network topologies and compared the results to three baselines. The results demonstrate that our approach exhibits superior performance in the distribution of circuits across diverse topologies when compared to the established baselines.

Author:

Simon Schlichting

Advisors:

Leo Sünkel, Maximilian Zorn, Claudia Linnhoff-Popien

Student Thesis | Published December 2024 | Copyright © QAR-Lab
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Reinforcement learning-supported state preparation using parameterized quantum gates

Reinforcement learning-supported state preparation using parameterized quantum gates

Abstract:

This thesis investigates the application of reinforcement learning (RL) in order to optimize the state preparation in parameterized quantum circuits. By using RL algorithms, an agent is trained to find the optimal sequence of quantum gates so as to reconstruct predetermined target states. Particular attention is paid to the challenges of using parametric gates, which require continuous optimization when compared to discrete circuits. Dierent approaches, including one- and two-stage methods as well as hyperparameter optimizations, are evaluated experimentally. The results show that RL-based methods can successfully contribute to the reduction of circuit depth, however this applies mainly to simple circuits. More complex circuits require deeper adaptations of the optimization strategy in order to achieve similar success.

Author:

Isabella Debelic

Advisors:

Michael Kölle, Philipp Altmann, Claudia Linnhoff-Popien

Student Thesis | Published December 2024 | Copyright © QAR-Lab
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