Student-Abstracts-EN

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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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Comparison of different hybrid quantum machine learning approaches for image classification on quantum computers

Comparison of different hybrid quantum machine learning approaches for image classification on quantum computers

Abstract:

Nowadays, Machine learning (ML) and the classification of images are becoming increasingly important. ML is used amongst others in autonomous vehicles to determine obstacles or in medicine for the automatic detection of diseases. However, the demands on neural networks used for image classification are constantly increasing as the features in the images become more and more complex. A promising solution in this area is quantum computing, or more precisely quantum machine learning (QML). Due to the advantages that qubits used in quantum computers bring with them, QML approaches could achieve significantly faster and better results than conventional ML methods. Quantum computing is currently in the so-called ’noisy intermediate-scale quantum’ (NISQ) era which means that quantum computers only have a few qubits, which are prone to errors. Accordingly, quantum machine learning cannot be easily implemented. The solution are hybrid approaches that use classical structures and combine them with quantum circuits.

This work analyzes the hybrid approaches Quanvolutional Neural Network (QCNN), Quantum Transfer Learning (QTL) and Variational Quantum Circuit (VQC). These are trained to classify the images of the MNIST data set. The training is takes place several times with different seeds in order to test the robustness of the approaches. They are then compared based on accuracy, loss and training duration. Additionally, a conventional Convolutional Neural Network (CNN) is used for comparison. Finally, the most efficient approach will be determined. The evaluation of the experiment shows that the QCNN achieves significantly better results than QTL and VQC. However, the conventional CNN performs better than the QCNN in all metrics.

Author:

Nicolas Holeczek

Advisors:

Leo Sünkel, Philipp Altmann, Claudia Linnhoff-Popien

Student Thesis | Published December 2024 | Copyright © QAR-Lab
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Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis

Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis

Abstract:

Quantum computing has the potential to solve complex problems that are intractable for classical computers, while serving as a cornerstone of next-generation systems offering extreme computational power. This capability arises from the unique properties of qubits and quantum parallelism, allowing quantum computers to perform certain calculations much faster than classical counterparts.
The optimization of quantum circuits is essential for advancing quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices. These devices face significant challenges due to their limited number of qubits and high error rates, making efficient circuit synthesis critical. Genetic algorithms (GAs) have emerged as a promising solution for optimizing quantum circuits by automating a task that is otherwise manually solved in an inefficient manner.
This thesis investigates the impact of various mutation strategies within a GA frame- work for quantum circuit synthesis. Mutations interact at the most fundamental level of a circuit and can significantly influence overall performance. Collecting data on how these mutations transform circuits and determining which strategies are most efficient is a key step in developing a robust GA optimizer for quantum synthesis.
The experiments conducted in this research employed a fitness function primarily based on fidelity, while also considering circuit depth and the number of T operations. The experiments focused on optimizing four to six qubit circuits with extensive hyperparameter testing to identify optimal solutions for practical quantum computing. The results indicate that the combination of delete and swap strategies, without employing change or add strategies, provided the best performance under the given constraints.

Author:

Tom Bintener

Advisors:

Michael Kölle, Maximilian Zorn, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published December 2024 | Copyright © QAR-Lab
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Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning: Evolutionary Strategies for Optimization

Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning: Evolutionary Strategies for Optimization

Abstract:

The field of Multi-Agent Reinforcement Learning (MARL) is becoming increasingly relevant in domains that involve the interaction of multiple agents, such as autonomous driving and robotics. One challenge in MARL is the exponential growth of dimensions in the state and action spaces. Quantum properties o!er a solution by enabling compact data processing and reducing trainable parameters. One drawback of gradient-based optimization methods in Quantum MARL is the possibility of Barren Plateaus impeding effective parameter updating, thereby hindering convergence. Evolutionary Algorithms, however, bypass this issue as they do not rely on gradient information. Building on research that demonstrates the potential of Evolutionary Algorithms in optimizing Variational Quantum Circuits for MARL tasks, we examine how introducing architectural changes into the evolutionary process affects optimization. We explore three different architecture concepts for Variational Quantum Circuits — Layer-Based, Gate-Based, and Prototype-Based — by applying two evolutionary strategies: one involving both recombination and mutation (ReMu), and the other using mutation only (Mu). To evaluate the efficacy of these approaches, we tested them in the Coin Game, comparing them to a baseline without architectural modifications. The mutation-only strategy with the Gate- Based approach yielded the best results, achieving the highest scores, number of coins collected, and own coin rates while using the fewest parameters. Furthermore, a variant of the Gate-Based approach with results comparable to those of the baseline required significantly fewer gates, resulting in an acceleration of the runtime by 90.1%.

Author:

Karola Schneider

Advisors:

Michael Kölle, Leo Sünkel, Claudia Linnhoff-Popien

Student Thesis | Published November 2024 | Copyright © QAR-Lab
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The Trainability of Quantum FederatedLearning

The Trainability of Quantum Federated Learning

Abstract:

This thesis explores the implementation and evaluation of Quantum Federated Learning (QFL), where Variational Quantum Circuits (VQCs) are collaboratively trained across multiple quantum clients. The primary focus is on comparing the performance and trainability of QFL with traditional non-federated quantum machine learning approaches using the MNIST dataset. Experiments were conducted with 2, 3, 4, and 5 clients, each processing different subsets of data, and with varying numbers of layers (1, 2, and 4) in the quantum circuits. The trainability of the models was assessed through the evaluation of accuracy, loss, and gradient norms throughout the training process. The results demonstrate that while QFL enables collaborative learning and shows significant improvements in these metrics during training, the baseline models without federated learning generally exhibit superior performance in terms of final accuracy and loss due to the uninterrupted optimization process. Additionally, the impact of increasing the number of layers on training stability and performance was examined.

Author:

Sina Mohammad Rezaei

Advisors:

Leo Sünkel, Thomas Gabor, Tobias Rohe, Claudia Linnhoff-Popien

Student Thesis | Published November 2024 | Copyright © QAR-Lab
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Investigating the Lottery Ticket Hypothesis for Variational Quantum Circuits

Investigating the Lottery Ticket Hypothesis for Variational Quantum Circuits

Abstract:

Quantum computing is an emerging field in computer science that has made significant progress in recent years, including in the area of machine learning. Through the principles of quantum physics, it offers the possibility of overcoming the limitations of classical algorithms. However, variational quantum circuits (VQCs), a specific type of quantum circuits utilizing varying parameters, face a significant challenge from the barren plateau phenomenon, which can hinder the optimization process in certain cases. The Lottery Ticket Hypothesis (LTH) is a recent concept in classical machine learning that has led to notable improvements in neural networks. In this thesis, we investigate whether it can be applied to VQCs. The LTH claims that within a large neural network, there exists a smaller, more efficient subnetwork (a “winning ticket”) that can achieve comparable performance. Applying this approach to VQCs could help reduce the impact of the barren plateau problem. The results of this thesis show that the weak LTH can be applied to VQCs, with winning tickets discovered that retain as little as 26.0% of the original weights. For the strong LTH, where a pruning mask is learned without any training, we found a winning ticket for a binary VQC, performing at 100% accuracy with 45% remaining weights. This shows that the strong LTH is also applicable to VQCs. These findings provide initial evidence that the LTH may be a valuable tool for improving the efficiency and performance of VQCs in quantum machine learning tasks.

Author:

Leonhard Klingert

Advisors:

Michael Kölle, Julian Schönberger, Claudia Linnhoff-Popien

Student Thesis | Published November 2024 | Copyright © QAR-Lab
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State Preparation on Quantum HardwareUsing an Island Genetic Algorithm

State Preparation on Quantum Hardware Using an Island Genetic Algorithm

Abstract:

As genetic algorithms demonstrate a remarkable versatility and extensive range of applications, their utilisation in the context of quantum circuit synthesis remains a notable area of interest. Given the considerable challenge presented by the vast search space inherent to quantum circuit generation, the theoretical suitability of genetic algorithms is evident, particularly in view of their intrinsic exploration capability. In addition to the utilisation of quantum algorithms for the attainment of up to exponential runtime advantages, all such algorithms necessitate the preparation of specific states in order to confer said advantages. It is therefore crucial to be able to create specific states, even in the absence of knowledge regarding the underlying circuits. One notable state is the Greenberger–Horne–Zeilinger (GHZ) state, which unites the superposition and entanglement characteristics inherent to quantum computing. Accordingly, this circuit is used as the target state for reproduction in this thesis, and two additional circuits with distinctive states are employed to illustrate the general applicability of this approach. Additionally, the genetic algorithm is executed not only on the simulator but also on the IONQ Aria-1 quantum processing unit (QPU).

This thesis elucidates the distinctions between the population-based and the island-based approach. These approaches differ in terms of whether the individuals are part of a single population or whether they develop separately into smaller groups dispersed across multiple islands and interact with each other solely through a process of migration between the islands. This thesis presents evidence of the superiority of the island-based approach in comparison to the population-based approach for the GHZ-state, as well as the two other circuits. Moreover, it demonstrates that the constraints of the hardware execution could be met by employing the island-based approach on the IONQ Aria-1 QPU to generate a solution candidate for the GHZ-state. Furthermore, the provenance of the generated solution candidates indicates the efficacy of the genetic algorithm itself and also the enhanced diversity of the different approaches.

Author:

Jonathan Philip Wulf

Advisors:

Jonas Stein, Maximilian Zorn, Claudia Linnhoff-Popien

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