Abstracts-QO-EN

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

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

Abstract:

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

Author:

Timo Witter

Advisors:

Michael Kölle, Philipp Altmann, Claudia Linnhoff-Popien

Student Thesis | Published February 2024 | Copyright © QAR-Lab
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Construction of quantum circuits with restricted gates

Construction of quantum circuits with restricted gates

Abstract:

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

Author:

Sebastian Wölckert

Advisors:

Maximilian Balthasar Mansky, Sebastian Zielinski, Claudia Linnhoff-Popien

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

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

Abstract:

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

Author:

Afrae Ahouzi

Advisors:

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

Student Thesis | Published November 2023 | Copyright © QAR-Lab
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Application of graph partitioning algorithms and genetic algorithms to optimize teleportation costs in distributed quantum circuits.

Application of graph partitioning algorithms and genetic algorithms to optimize teleportation costs in distributed quantum circuits.

Abstract:

Currently, we are in the Noisy Intermediate Scale Quantum (NISQ) era, where the number of qubits that can be used in a single quantum computer is increasing. However, with this development come challenges in handling large quantum systems. Distributed quantum computation is therefore gaining importance to overcome these challenges. In this process, multiple quantum computers or quantum processing units are connected to work together on a problem. This enables the use of larger computational capacities and more efficient solutions to complex tasks. In distributed quantum computing, different units or subsystems communicate with each other to exchange quantum information. The basic teleportation protocol plays an important role in this process. It enables the transfer of quantum information between subsystems. An important aspect is to minimize the number of teleportations. Thus, the aim is to increase the accuracy of quantum computations, reduce the error-proneness of qubits, and at the same time make resource consumption more efficient.In this work, different graph partitioning algorithms, such as the Kernighan-Lin algorithm and spectral partitioning, a genetic algorithm (GA), and two hybrid genetic algorithms (HGA), which are a combination of the graph partitioning algorithms and a GA, are applied and investigated to minimize the number of global quantum gates and the associated teleportation costs. First, the graph partitioning algorithms are used to partition the nodes as uniformly as possible. In addition, a GA is implemented to take care of the partitioning of qubits using random partitions. The two HGAs lead to a near-optimal arrangement of the global quantum gates after the qubits are partitioned using the graph partitioning algorithms. Finally, the proposed approaches are investigated using nine benchmark circuits and compared in terms of the number of global quantum gates and teleportation costs. Random searches are also performed for the GA and the two HGAs to verify their performance with respect to the optimization objective. The results indicate a significant improvement in teleportation cost.

Author:

Teodor Slaveykov

Advisors:

Leo Sünkel Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published August 2023 | Copyright © QAR-Lab
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NISQ-ready community detection on weighted graphs using separation-node identification

NISQ-ready community detection on weighted graphs using separation-node identification

Abstract:

An important optimization problem in computer science is the detection of communities. By analyzing networks, so-called communities can be found and important information in many fields – from biology to social structures – can be derived. By weighting individual edges, even more information can be processed than by the mere presence of these edges. However, for community detection on weighted graphs, more factors must be considered as a result. Since this is an NP-hard optimization problem, heuristics are often used to find an acceptable solution faster and more efficiently. One promising approach is the use of quantum computers, as it has already been experimentally shown that they can achieve more efficient results than classical computers in certain domains (e.g., Grover or Shor algorithm). However, since most approaches to community detection using QUBO matrices consume a lot of memory, the goal of this work is to find an approach with a good memory efficiency. To this end, this work presents a promising community detection approach based on the detection and analysis of separation nodes, which has the advantage that the dimensions of the resulting QUBO matrix do not exceed the number of nodes and the matrix itself is as sparse as the adjacency matrix of the graph. These separating nodes are designed to divide the graph when they are removed such that the remaining components are each exactly part of a community. This approach is extended to weighted graphs by determining the probability that an edge is a separating edge based on the information flow of the neighborhood. This approach is tested using synthesized graphs with a fixed ground truth about their communities, to which weights are assigned without changing the community structure.

Translated with www.DeepL.com/Translator (free version)

Author:

Dominik Ott

Advisors:

Jonas Stein, Jonas Nüßlein, Claudia Linnhoff-Popien

Student Thesis | Published August 2023 | Copyright © QAR-Lab
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Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs (en)

Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs

Abstract:

Quantum walks, a quantum analog of classical random walks, have emerged as a powerful paradigm in quantum computation and simulation. While classical random walks rely on stochastic processes to explore systems, quantum walks leverage the unique properties of quantum mechanics to perform these tasks more efficiently. In particular, discrete-time quantum walks (DTQWs) have been studied extensively for their applications in graph theory, such as graph isomorphism, graph connectivity, and graph-based search problems. Despite their potential, implementing DTQWs on near-term quantum devices remains challenging. While previous works have focused on quantum circuit implementations for DTQWs with uniform coin operators, implementing non-homogeneous coin sets is a complex task that requires new approaches. This thesis presents an efficient quantum circuit architecture for implementing coined DTQWs with non-homogeneous, position-dependent coin sets on a large subset of bipartite graphs. A novel edge labeling scheme, Gray Code Directed Edges encoding, is introduced, taking advantage of Gray code for position encoding and the bipartite structure of the underlying graph to minimize the complexity of the quantum circuits representing coin and shift operators. This optimization leads to fewer gate operations, reducing the impact of noise and errors in near-term quantum devices. A labeling scheme is developed for various graph topologies, including cycle graphs, chained cylinder graphs, and square grid graphs, which are especially relevant for reinforcement learning applications. These findings offer a new perspective on the implementation of coined quantum walks and lay a foundation for future research on quantum walks with non-homogeneous coin sets.

Author:

Viktoryia Patapovich

Advisors:

Jonas Stein, Michael Kölle, Maximilian-Balthasar Mansky, Claudia Linnhoff-Popien

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